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Axiom

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word, meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.

The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning.

In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example a + 0 = a in integer arithmetic.

Non-logical axioms may also be called "postulates", "assumptions" or "proper axioms". In most cases, a non-logical axiom is simply a formal logical expression used in deduction to build a mathematical theory, and might or might not be self-evident in nature (e.g., the parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms), and there are typically many ways to axiomatize a given mathematical domain.

Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics.

Etymology
The word axiom comes from the Greek word ἀξίωμα (axíōma), a verbal noun from the verb ἀξιόειν (axioein), meaning "to deem worthy", but also "to require", which in turn comes from ἄξιος (áxios), meaning "being in balance", and hence "having (the same) value (as)", "worthy", "proper". Among the ancient Greek philosophers and mathematicians, axioms were taken to be immediately evident propositions, foundational and common to many fields of investigation, and self-evidently true without any further argument or proof.

The root meaning of the word postulate is to "demand"; for instance, Euclid demands that one agree that some things can be done (e.g., any two points can be joined by a straight line).

Ancient geometers maintained some distinction between axioms and postulates. While commenting on Euclid's books, Proclus remarks that "Geminus held that this [4th] Postulate should not be classed as a postulate but as an axiom, since it does not, like the first three Postulates, assert the possibility of some construction but expresses an essential property." Boethius translated 'postulate' as petitio and called the axioms notiones communes but in later manuscripts this usage was not always strictly kept.

Early Greeks
The logico-deductive method whereby conclusions (new knowledge) follow from premises (old knowledge) through the application of sound arguments (syllogisms, rules of inference) was developed by the ancient Greeks, and has become the core principle of modern mathematics. Tautologies excluded, nothing can be deduced if nothing is assumed. Axioms and postulates are thus the basic assumptions underlying a given body of deductive knowledge. They are accepted without demonstration. All other assertions (theorems, in the case of mathematics) must be proven with the aid of these basic assumptions. However, the interpretation of mathematical knowledge has changed from ancient times to the modern, and consequently the terms axiom and postulate hold a slightly different meaning for the present day mathematician, than they did for Aristotle and Euclid.

The ancient Greeks considered geometry as just one of several sciences, and held the theorems of geometry on par with scientific facts. As such, they developed and used the logico-deductive method as a means of avoiding error, and for structuring and communicating knowledge. Aristotle's posterior analytics is a definitive exposition of the classical view.

An "axiom", in classical terminology, referred to a self-evident assumption common to many branches of science. A good example would be the assertion that: "When an equal amount is taken from equals, an equal amount results."

At the foundation of the various sciences lay certain additional hypotheses that were accepted without proof. Such a hypothesis was termed a postulate. While the axioms were common to many sciences, the postulates of each particular science were different. Their validity had to be established by means of real-world experience. Aristotle warns that the content of a science cannot be successfully communicated if the learner is in doubt about the truth of the postulates.

The classical approach is well-illustrated by Euclid's Elements, where a list of postulates is given (common-sensical geometric facts drawn from our experience), followed by a list of "common notions" (very basic, self-evident assertions).

 * Postulates
 * It is possible to draw a straight line from any point to any other point.
 * It is possible to extend a line segment continuously in both directions.
 * It is possible to describe a circle with any center and any radius.
 * It is true that all right angles are equal to one another.
 * ("Parallel postulate") It is true that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, intersect on that side on which are the angles less than the two right angles.

 * Common notions:
 * Things which are equal to the same thing are also equal to one another.
 * If equals are added to equals, the wholes are equal.
 * If equals are subtracted from equals, the remainders are equal.
 * Things which coincide with one another are equal to one another.
 * The whole is greater than the part.

Modern development
A lesson learned by mathematics in the last 150 years is that it is useful to strip the meaning away from the mathematical assertions (axioms, postulates, propositions, theorems) and definitions. One must concede the need for primitive notions, or undefined terms or concepts, in any study. Such abstraction or formalization makes mathematical knowledge more general, capable of multiple different meanings, and therefore useful in multiple contexts. Alessandro Padoa, Mario Pieri, and Giuseppe Peano were pioneers in this movement.

Structuralist mathematics goes further, and develops theories and axioms (e.g. field theory, group theory, topology, vector spaces) without any particular application in mind. The distinction between an "axiom" and a "postulate" disappears. The postulates of Euclid are profitably motivated by saying that they lead to a great wealth of geometric facts. The truth of these complicated facts rests on the acceptance of the basic hypotheses. However, by throwing out Euclid's fifth postulate, one can get theories that have meaning in wider contexts (e.g., hyperbolic geometry). As such, one must simply be prepared to use labels such as "line" and "parallel" with greater flexibility. The development of hyperbolic geometry taught mathematicians that it is useful to regard postulates as purely formal statements, and not as facts based on experience.

When mathematicians employ the field axioms, the intentions are even more abstract. The propositions of field theory do not concern any one particular application; the mathematician now works in complete abstraction. There are many examples of fields; field theory gives correct knowledge about them all.

It is not correct to say that the axioms of field theory are "propositions that are regarded as true without proof." Rather, the field axioms are a set of constraints. If any given system of addition and multiplication satisfies these constraints, then one is in a position to instantly know a great deal of extra information about this system.

Modern mathematics formalizes its foundations to such an extent that mathematical theories can be regarded as mathematical objects, and mathematics itself can be regarded as a branch of logic. Frege, Russell, Poincaré, Hilbert, and Gödel are some of the key figures in this development.

Another lesson learned in modern mathematics is to examine purported proofs carefully for hidden assumptions.

In the modern understanding, a set of axioms is any collection of formally stated assertions from which other formally stated assertions follow – by the application of certain well-defined rules. In this view, logic becomes just another formal system. A set of axioms should be consistent; it should be impossible to derive a contradiction from the axioms. A set of axioms should also be non-redundant; an assertion that can be deduced from other axioms need not be regarded as an axiom.

It was the early hope of modern logicians that various branches of mathematics, perhaps all of mathematics, could be derived from a consistent collection of basic axioms. An early success of the formalist program was Hilbert's formalization of Euclidean geometry, and the related demonstration of the consistency of those axioms.

In a wider context, there was an attempt to base all of mathematics on Cantor's set theory. Here, the emergence of Russell's paradox and similar antinomies of naïve set theory raised the possibility that any such system could turn out to be inconsistent.

The formalist project suffered a setback a century ago, when Gödel showed that it is possible, for any sufficiently large set of axioms (Peano's axioms, for example) to construct a statement whose truth is independent of that set of axioms. As a corollary, Gödel proved that the consistency of a theory like Peano arithmetic is an unprovable assertion within the scope of that theory.

It is reasonable to believe in the consistency of Peano arithmetic because it is satisfied by the system of natural numbers, an infinite but intuitively accessible formal system. However, at present, there is no known way of demonstrating the consistency of the modern Zermelo–Fraenkel axioms for set theory. Furthermore, using techniques of forcing (Cohen) one can show that the continuum hypothesis (Cantor) is independent of the Zermelo–Fraenkel axioms. Thus, even this very general set of axioms cannot be regarded as the definitive foundation for mathematics.

Other sciences
Experimental sciences - as opposed to mathematics and logic - also have general founding assertions from which a deductive reasoning can be built so as to express propositions that predict properties - either still general or much more specialized to a specific experimental context. For instance, Newton's laws in classical mechanics, Maxwell's equations in classical electromagnetism, Einstein's equation in general relativity, Mendel's laws of genetics, Darwin's Natural selection law, etc. These founding assertions are usually called principles or postulates so as to distinguish from mathematical axioms.

As a matter of facts, the role of axioms in mathematics and postulates in experimental sciences is different. In mathematics one neither "proves" nor "disproves" an axiom. A set of mathematical axioms gives a set of rules that fix a conceptual realm, in which the theorems logically follow. In contrast, in experimental sciences, a set of postulates shall allow deducing results that match or do not match experimental results. If postulates do not allow deducing experimental predictions, they do not set a scientific conceptual framework and have to be completed or made more accurate. If the postulates allow deducing predictions of experimental results, the comparison with experiments allows falsifying (falsified) the theory that the postulates install. A theory is considered valid as long as it has not been falsified.

Now, the transition between the mathematical axioms and scientific postulates is always slightly blurred, especially in physics. This is due to the heavy use of mathematical tools to support the physical theories. For instance, the introduction of Newton's laws rarely establishes as a prerequisite neither Euclidean geometry or differential calculus that they imply. It became more apparent when Albert Einstein first introduced special relativity where the invariant quantity is no more the Euclidean length $$l$$ (defined as $$l^2 = x^2 + y^2 + z^2$$) > but the Minkowski spacetime interval $$s$$ (defined as $$s^2 = c^2 t^2 - x^2 - y^2 - z^2$$), and then general relativity where flat Minkowskian geometry is replaced with pseudo-Riemannian geometry on curved manifolds.

In quantum physics, two sets of postulates have coexisted for some time, which provide a very nice example of falsification. The 'Copenhagen school' (Niels Bohr, Werner Heisenberg, Max Born) developed an operational approach with a complete mathematical formalism that involves the description of quantum system by vectors ('states') in a separable Hilbert space, and physical quantities as linear operators that act in this Hilbert space. This approach is fully falsifiable and has so far produced the most accurate predictions in physics. But it has the unsatisfactory aspect of not allowing answers to questions one would naturally ask. For this reason, another 'hidden variables' approach was developed for some time by Albert Einstein, Erwin Schrödinger, David Bohm. It was created so as to try to give deterministic explanation to phenomena such as entanglement. This approach assumed that the Copenhagen school description was not complete, and postulated that some yet unknown variable was to be added to the theory so as to allow answering some of the questions it does not answer (the founding elements of which were discussed as the EPR paradox in 1935). Taking this idea seriously, John Bell derived in 1964 a prediction that would lead to different experimental results (Bell's inequalities) in the Copenhagen and the Hidden variable case. The experiment was conducted first by Alain Aspect in the early 1980's, and the result excluded the simple hidden variable approach (sophisticated hidden variables could still exist but their properties would still be more disturbing than the problems they try to solve). This does not mean that the conceptual framework of quantum physics can be considered as complete now, since some open questions still exist (the limit between the quantum and classical realms, what happens during a quantum measurement, what happens in a completely closed quantum system such as the universe itself, etc.).

Mathematical logic
In the field of mathematical logic, a clear distinction is made between two notions of axioms: logical and non-logical (somewhat similar to the ancient distinction between "axioms" and "postulates" respectively).

Logical axioms
These are certain formulas in a formal language that are universally valid, that is, formulas that are satisfied by every assignment of values. Usually one takes as logical axioms at least some minimal set of tautologies that is sufficient for proving all tautologies in the language; in the case of predicate logic more logical axioms than that are required, in order to prove logical truths that are not tautologies in the strict sense.

Propositional logic
In propositional logic it is common to take as logical axioms all formulae of the following forms, where $$\phi$$, $$\chi$$, and $$\psi$$ can be any formulae of the language and where the included primitive connectives are only "$$\neg$$" for negation of the immediately following proposition and "$$\to$$" for implication from antecedent to consequent propositions:

 * 1) $$\phi \to (\psi \to \phi)$$
 * 2) $$(\phi \to (\psi \to \chi)) \to ((\phi \to \psi) \to (\phi \to \chi))$$
 * 3) $$(\lnot \phi \to \lnot \psi) \to (\psi \to \phi).$$

Each of these patterns is an axiom schema, a rule for generating an infinite number of axioms. For example, if $$A$$, $$B$$, and $$C$$ are propositional variables, then $$A \to (B \to A)$$ and $$(A \to \lnot B) \to (C \to (A \to \lnot B))$$ are both instances of axiom schema 1, and hence are axioms. It can be shown that with only these three axiom schemata and modus ponens, one can prove all tautologies of the propositional calculus. It can also be shown that no pair of these schemata is sufficient for proving all tautologies with modus ponens.

Other axiom schemata involving the same or different sets of primitive connectives can be alternatively constructed.

These axiom schemata are also used in the predicate calculus, but additional logical axioms are needed to include a quantifier in the calculus.

First-order logic
Axiom of Equality. Let $$\mathfrak{L}$$ be a first-order language. For each variable $$x$$, the below formula is universally valid.

$$x = x$$

This means that, for any variable symbol $$x$$, the formula $$x = x$$ can be regarded as an axiom. Also, in this example, for this not to fall into vagueness and a never-ending series of "primitive notions", either a precise notion of what we mean by $$x = x$$ (or, for that matter, "to be equal") has to be well established first, or a purely formal and syntactical usage of the symbol $$=$$ has to be enforced, only regarding it as a string and only a string of symbols, and mathematical logic does indeed do that.

Another, more interesting example axiom scheme, is that which provides us with what is known as Universal Instantiation:

Axiom scheme for Universal Instantiation. Given a formula $$\phi$$ in a first-order language $$\mathfrak{L}$$, a variable $$x$$ and a term $$t$$ that is substitutable for $$x$$ in $$\phi$$, the below formula is universally valid.

$$\forall x \, \phi \to \phi^x_t$$

Where the symbol $$\phi^x_t$$ stands for the formula $$\phi$$ with the term $$t$$ substituted for $$x$$. (See Substitution of variables.) In informal terms, this example allows us to state that, if we know that a certain property $$P$$ holds for every $$x$$ and that $$t$$ stands for a particular object in our structure, then we should be able to claim $$P(t)$$. Again, we are claiming that the formula $$\forall x \phi \to \phi^x_t$$ is valid, that is, we must be able to give a "proof" of this fact, or more properly speaking, a metaproof. These examples are metatheorems of our theory of mathematical logic since we are dealing with the very concept of proof itself. Aside from this, we can also have Existential Generalization:

Axiom scheme for Existential Generalization. Given a formula $$\phi$$ in a first-order language $$\mathfrak{L}$$, a variable $$x$$ and a term $$t$$ that is substitutable for $$x$$ in $$\phi$$, the below formula is universally valid.

$$\phi^x_t \to \exists x \, \phi$$

Non-logical axioms
Non-logical axioms are formulas that play the role of theory-specific assumptions. Reasoning about two different structures, for example, the natural numbers and the integers, may involve the same logical axioms; the non-logical axioms aim to capture what is special about a particular structure (or set of structures, such as groups). Thus non-logical axioms, unlike logical axioms, are not tautologies. Another name for a non-logical axiom is postulate.

Almost every modern mathematical theory starts from a given set of non-logical axioms, and it was thought that, in principle, every theory could be axiomatized in this way and formalized down to the bare language of logical formulas.

Non-logical axioms are often simply referred to as axioms in mathematical discourse. This does not mean that it is claimed that they are true in some absolute sense. For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom, we can do quite well developing (the more general) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.

Thus, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system.

Examples
This section gives examples of mathematical theories that are developed entirely from a set of non-logical axioms (axioms, henceforth). A rigorous treatment of any of these topics begins with a specification of these axioms.

Basic theories, such as arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that the axioms being used are the axioms of Zermelo–Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann–Bernays–Gödel set theory, a conservative extension of ZFC. Sometimes slightly stronger theories such as Morse–Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe is used, but in fact, most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.

The study of topology in mathematics extends all over through point set topology, algebraic topology, differential topology, and all the related paraphernalia, such as homology theory, homotopy theory. The development of abstract algebra brought with itself group theory, rings, fields, and Galois theory.

This list could be expanded to include most fields of mathematics, including measure theory, ergodic theory, probability, representation theory, and differential geometry.

Arithmetic
The Peano axioms are the most widely used axiomatization of first-order arithmetic. They are a set of axioms strong enough to prove many important facts about number theory and they allowed Gödel to establish his famous second incompleteness theorem.

We have a language $$\mathfrak{L}_{NT} = \{0, S\}$$ where $$0$$ is a constant symbol and $$S$$ is a unary function and the following axioms:

 * 1) $$\forall x. \lnot (Sx = 0) $$
 * 2) $$\forall x. \forall y. (Sx = Sy \to x = y) $$
 * 3) $$(\phi(0) \land \forall x.\,(\phi(x) \to \phi(Sx))) \to \forall x.\phi(x)$$ for any $$\mathfrak{L}_{NT}$$ formula $$\phi$$ with one free variable.

The standard structure is $$\mathfrak{N} = \langle\N, 0, S\rangle$$ where $$\N$$ is the set of natural numbers, $$S$$ is the successor function and $$0$$ is naturally interpreted as the number 0.

Euclidean geometry
Probably the oldest, and most famous, list of axioms are the 4 + 1 Euclid's postulates of plane geometry. The axioms are referred to as "4 + 1" because for nearly two millennia the fifth (parallel) postulate ("through a point outside a line there is exactly one parallel") was suspected of being derivable from the first four. Ultimately, the fifth postulate was found to be independent of the first four. One can assume that exactly one parallel through a point outside a line exists, or that infinitely many exist. This choice gives us two alternative forms of geometry in which the interior angles of a triangle add up to exactly 180 degrees or less, respectively, and are known as Euclidean and hyperbolic geometries. If one also removes the second postulate ("a line can be extended indefinitely") then elliptic geometry arises, where there is no parallel through a point outside a line, and in which the interior angles of a triangle add up to more than 180 degrees.

Real analysis
The objectives of the study are within the domain of real numbers. The real numbers are uniquely picked out (up to isomorphism) by the properties of a Dedekind complete ordered field, meaning that any nonempty set of real numbers with an upper bound has a least upper bound. However, expressing these properties as axioms requires the use of second-order logic. The Löwenheim–Skolem theorems tell us that if we restrict ourselves to first-order logic, any axiom system for the reals admits other models, including both models that are smaller than the reals and models that are larger. Some of the latter are studied in non-standard analysis.

Deductive systems and completeness
A deductive system consists of a set $$\Lambda$$ of logical axioms, a set $$\Sigma$$ of non-logical axioms, and a set $$\{(\Gamma, \phi)\}$$ of rules of inference. A desirable property of a deductive system is that it be complete. A system is said to be complete if, for all formulas $$\phi$$, $$\text{if }\Sigma \models \phi\text{ then }\Sigma \vdash \phi$$

that is, for any statement that is a logical consequence of $$\Sigma$$ there actually exists a deduction of the statement from $$\Sigma$$. This is sometimes expressed as "everything that is true is provable", but it must be understood that "true" here means "made true by the set of axioms", and not, for example, "true in the intended interpretation". Gödel's completeness theorem establishes the completeness of a certain commonly used type of deductive system.

Note that "completeness" has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms $$\Sigma$$ of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement $$\phi$$ such that neither $$\phi$$ nor $$\lnot\phi$$ can be proved from the given set of axioms.

There is thus, on the one hand, the notion of completeness of a deductive system and on the other hand that of completeness of a set of non-logical axioms. The completeness theorem and the incompleteness theorem, despite their names, do not contradict one another.

Further discussion
Early mathematicians regarded axiomatic geometry as a model of physical space, and obviously, there could only be one such model. The idea that alternative mathematical systems might exist was very troubling to mathematicians of the 19th century and the developers of systems such as Boolean algebra made elaborate efforts to derive them from traditional arithmetic. Galois showed just before his untimely death that these efforts were largely wasted. Ultimately, the abstract parallels between algebraic systems were seen to be more important than the details, and modern algebra was born. In the modern view, axioms may be any set of formulas, as long as they are not known to be inconsistent.

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Alpha

Alpha (uppercase, lowercase ) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph, which is the West Semitic word for "ox". Letters that arose from alpha include the Latin letter A and the Cyrillic letter А.

Greek
In Ancient Greek, alpha was pronounced and could be either phonemically long ([aː]) or short ([a]). Where there is ambiguity, long and short alpha are sometimes written with a macron and breve today: Ᾱᾱ, Ᾰᾰ.
 * = ὥρᾱ hōrā "a time"
 * = γλῶσσᾰ glôssa "tongue"

In Modern Greek, vowel length has been lost, and all instances of alpha simply represent the open front unrounded vowel.

In the polytonic orthography of Greek, alpha, like other vowel letters, can occur with several diacritic marks: any of three accent symbols (ά, ὰ, ᾶ), and either of two breathing marks (ἁ, ἀ), as well as combinations of these. It can also combine with the iota subscript (ᾳ).

Greek grammar
In the Attic–Ionic dialect of Ancient Greek, long alpha fronted to  (eta). In Ionic, the shift took place in all positions. In Attic, the shift did not take place after epsilon, iota, and rho (ε, ι, ρ; e, i, r). In Doric and Aeolic, long alpha is preserved in all positions.
 * Doric, Aeolic, Attic χώρᾱ chṓrā – Ionic χώρη chṓrē, "country"
 * Doric, Aeolic φᾱ́μᾱ phā́mā – Attic, Ionic φήμη phḗmē, "report"

Privative a is the Ancient Greek prefix ἀ- or ἀν- a-, an-, added to words to negate them. It originates from the Proto-Indo-European * (syllabic nasal) and is cognate with English un-.

Copulative a is the Greek prefix ἁ- or ἀ- ha-, a-. It comes from Proto-Indo-European *.

Mathematics and science
The letter alpha represents various concepts in physics and chemistry, including alpha radiation, angular acceleration, alpha particles, alpha carbon and strength of electromagnetic interaction (as fine-structure constant). Alpha also stands for thermal expansion coefficient of a compound in physical chemistry. It is also commonly used in mathematics in algebraic solutions representing quantities such as angles. Furthermore, in mathematics, the letter alpha is used to denote the area underneath a normal curve in statistics to denote significance level when proving null and alternative hypotheses. In ethology, it is used to name the dominant individual in a group of animals. In aerodynamics, the letter is used as a symbol for the angle of attack of an aircraft and the word "alpha" is used as a synonym for this property. In mathematical logic, α is sometimes used as a placeholder for ordinal numbers.

The proportionality operator "∝" (in Unicode: U+221D) is sometimes mistaken for alpha.

The uppercase letter alpha is not generally used as a symbol because it tends to be rendered identically to the uppercase A|Latin A.

International Phonetic Alphabet
In the International Phonetic Alphabet, the letter ɑ, which looks similar to the lower-case alpha, represents the open back unrounded vowel.

Origin
The Phoenician alphabet was adopted for Greek in the early 8th century BC, perhaps in Euboea. The majority of the letters of the Phoenician alphabet were adopted into Greek with much the same sounds as they had had in Phoenician, but ʼāleph, the Phoenician letter representing the glottal stop , was adopted as representing the vowel ; similarly, hē and ʽayin  are Phoenician consonants that became Greek vowels, epsilon  and omicron, respectively.

Plutarch
Plutarch, in Moralia, presents a discussion on why the letter alpha stands first in the alphabet. Ammonius asks Plutarch what he, being a Boeotian, has to say for Cadmus, the Phoenician who reputedly settled in Thebes and introduced the alphabet to Greece, placing alpha first because it is the Phoenician name for ox—which, unlike Hesiod, the Phoenicians considered not the second or third, but the first of all necessities. "Nothing at all," Plutarch replied. He then added that he would rather be assisted by Lamprias, his own grandfather, than by Dionysus' grandfather, i.e. Cadmus. For Lamprias had said that the first articulate sound made is "alpha", because it is very plain and simple—the air coming off the mouth does not require any motion of the tongue—and therefore this is the first sound that children make.

According to Plutarch's natural order of attribution of the vowels to the planets, alpha was connected with the Moon.

Alpha and Omega

As the first letter of the alphabet, Alpha as a Greek numeral came to represent the number 1. Therefore, Alpha, both as a symbol and term, is used to refer to the "first", or "primary", or "principal" (most significant) occurrence or status of a thing. The New Testament has God declaring himself to be the "Alpha and Omega, the beginning and the end, the first and the last." (Revelation 22:13, KJV, and see also 1:8).

Consequently, the term "alpha" has also come to be used to denote "primary" position in social hierarchy, examples being the concept of dominant "alpha" members in groups of animals.

Computer encodings

 * Greek alpha / Coptic alfa

For accented Greek characters, see Greek diacritics: Computer encoding.

 * Latin / IPA alpha

 * Mathematical / Technical alpha

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title: Alpha


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Alvin Toffler

Alvin Eugene Toffler (October 4, 1928 – June 27, 2016) was an American writer, futurist, and businessman known for his works discussing modern technologies, including the digital revolution and the communication revolution, with emphasis on their effects on cultures worldwide. He is regarded as one of the world's outstanding futurists.

Toffler was an associate editor of Fortune magazine. In his early works he focused on technology and its impact, which he termed "information overload". In 1970, his first major book about the future, Future Shock, became a worldwide best-seller and has sold over 6 million copies.

He and his wife Heidi Toffler (1929–2019), who collaborated with him for most of his writings, moved on to examining the reaction to changes in society with another best-selling book, The Third Wave, in 1980. In it, he foresaw such technological advances as cloning, personal computers, the Internet, cable television and mobile communication. His later focus, via their other best-seller, Powershift, (1990), was on the increasing power of 21st-century military hardware and the proliferation of new technologies.

He founded Toffler Associates, a management consulting company, and was a visiting scholar at the Russell Sage Foundation, visiting professor at Cornell University, faculty member of the New School for Social Research, a White House correspondent, and a business consultant. Toffler's ideas and writings were a significant influence on the thinking of business and government leaders worldwide, including China's Zhao Ziyang, and AOL founder Steve Case.

Early life
Alvin Toffler was born on October 4, 1928, in New York City, and raised in Brooklyn. He was the son of Rose (Albaum) and Sam Toffler, a furrier, both Polish Jews who had migrated to America. He had one younger sister. He was inspired to become a writer at the age of 7 by his aunt and uncle, who lived with the Tofflers. "They were Depression-era literary intellectuals," Toffler said, "and they always talked about exciting ideas."

Toffler graduated from New York University in 1950 as an English major, though by his own account he was more focused on political activism than grades. He met his future wife, Adelaide Elizabeth Farrell (nicknamed "Heidi"), when she was starting a graduate course in linguistics. Being radical students, they decided against further graduate work and moved to Cleveland, Ohio, where they married on April 29, 1950.

Career
Seeking experiences to write about, Alvin and Heidi Toffler spent the next five years as blue collar workers on assembly lines while studying industrial mass production in their daily work. He compared his own desire for experience to other writers, such as Jack London, who in his quest for subjects to write about sailed the seas, and John Steinbeck, who went to pick grapes with migrant workers. In their first factory jobs, Heidi became a union shop steward in the aluminum foundry where she worked. Alvin became a millwright and welder. In the evenings Alvin would write poetry and fiction, but discovered he was proficient at neither.

His hands-on practical labor experience helped Alvin Toffler land a position at a union-backed newspaper, a transfer to its Washington bureau in 1957, then three years as a White House correspondent, covering Congress and the White House for a Pennsylvania daily newspaper.

They returned to New York City in 1959 when Fortune magazine invited Alvin to become its labor columnist, later having him write about business and management. After leaving Fortune magazine in 1962, Toffler began a freelance career, writing long form articles for scholarly journals and magazines. His 1964 Playboy interviews with Russian novelist Vladimir Nabokov and Ayn Rand were considered among the magazine's best. His interview with Rand was the first time the magazine had given such a platform to a female intellectual, which as one commentator said, "the real bird of paradise Toffler captured for Playboy in 1964 was Ayn Rand."

Toffler was hired by IBM to conduct research and write a paper on the social and organizational impact of computers, leading to his contact with the earliest computer "gurus" and artificial intelligence researchers and proponents. Xerox invited him to write about its research laboratory and AT&T consulted him for strategic advice. This AT&T work led to a study of telecommunications, which advised the company's top management to break up the company more than a decade before the government forced AT&T to break up.

In the mid-1960s, the Tofflers began five years of research on what would become Future Shock, published in 1970. It has sold over 6 million copies worldwide, according to the New York Times, or over 15 million copies according to the Tofflers' Web site. Toffler coined the term "future shock" to refer to what happens to a society when change happens too fast, which results in social confusion and normal decision-making processes breaking down. The book has never been out of print and has been translated into dozens of languages.

He continued the theme in The Third Wave in 1980. While he describes the first and second waves as the agricultural and industrial revolutions, the "third wave," a phrase he coined, represents the current information, computer-based revolution. He forecast the spread of the Internet and email, interactive media, cable television, cloning, and other digital advancements. He claimed that one of the side effects of the digital age has been "information overload," another term he coined. In 1990, he wrote Powershift, also with the help of his wife, Heidi.

In 1996, with American business consultant Tom Johnson, they co-founded Toffler Associates, an advisory firm designed to implement many of the ideas the Tofflers had written on. The firm worked with businesses, NGOs, and governments in the United States, South Korea, Mexico, Brazil, Singapore, Australia, and other countries. During this period in his career, Toffler lectured worldwide, taught at several schools and met world leaders, such as Mikhail Gorbachev, along with key executives and military officials.

Ideas and opinions
Toffler stated many of his ideas during an interview with the Australian Broadcasting Corporation in 1998. "Society needs people who take care of the elderly and who know how to be compassionate and honest," he said. "Society needs people who work in hospitals. Society needs all kinds of skills that are not just cognitive; they're emotional, they're affectional. You can't run the society on data and computers alone."

His opinions about the future of education, many of which were in Future Shock, have often been quoted. An often misattributed quote, however, is that of psychologist Herbert Gerjuoy: "Tomorrow's illiterate will not be the man who can't read; he will be the man who has not learned how to learn."

Early in his career, after traveling to other countries, he became aware of the new and myriad inputs that visitors received from these other cultures. He explained during an interview that some visitors would become "truly disoriented and upset" by the strange environment, which he described as a reaction to culture shock. From that issue, he foresaw another problem for the future, when a culturally "new environment comes to you ... and comes to you rapidly." That kind of sudden cultural change within one's own country, which he felt many would not understand, would lead to a similar reaction, one of "future shock", which he wrote about in his book by that title. Toffler writes: "We must search out totally new ways to anchor ourselves, for all the old roots—religion, nation, community, family, or profession—are now shaking under the hurricane impact of the accelerative thrust."

In The Third Wave, Toffler describes three types of societies, based on the concept of "waves"—each wave pushes the older societies and cultures aside. He describes the "First Wave" as the society after agrarian revolution and replaced the first hunter-gatherer cultures. The "Second Wave," he labels society during the Industrial Revolution (ca. late 17th century through the mid-20th century). That period saw the increase of urban industrial populations which had undermined the traditional nuclear family, and initiated a factory-like education system, and the growth of the corporation. Toffler said:

"The Second Wave Society is industrial and based on mass production, mass distribution, mass consumption, mass education, mass media, mass recreation, mass entertainment, and weapons of mass destruction. You combine those things with standardization, centralization, concentration, and synchronization, and you wind up with a style of organization we call bureaucracy."

The "Third Wave" was a term he coined to describe the post-industrial society, which began in the late 1950s. His description of this period dovetails with other futurist writers, who also wrote about the Information Age, Space Age, Electronic Era, Global Village, terms which highlighted a scientific-technological revolution. The Tofflers claimed to have predicted a number of geopolitical events, such as the collapse of the Soviet Union, the fall of the Berlin Wall and the future economic growth in the Asia-Pacific region.

Influences and popular culture
Toffler often visited with dignitaries in Asia, including China's Zhao Ziyang, Singapore's Lee Kuan Yew and South Korea's Kim Dae Jung, all of whom were influenced by his views as Asia's emerging markets increased in global significance during the 1980s and 1990s. Although they had originally censored some of his books and ideas, China's government cited him along with Franklin Roosevelt and Bill Gates as being among the Westerners who had most influenced their country. The Third Wave along with a video documentary based on it became best-sellers in China and were widely distributed to schools. The video's success inspired the marketing of videos on related themes in the late 1990s by Infowars, whose name is derived from the term coined by Toffler in the book. Toffler's influence on Asian thinkers was summed up in an article in Daedalus, published by the American Academy of Arts & Sciences: "Where an earlier generation of Chinese, Korean, and Vietnamese revolutionaries wanted to re-enact the Paris Commune as imagined by Karl Marx, their post-revolutionary successors now want to re-enact Silicon Valley as imagined by Alvin Toffler."

U.S. House Speaker Newt Gingrich publicly lauded his ideas about the future, and urged members of Congress to read Toffler's book, Creating a New Civilization (1995). Others, such as AOL founder Steve Case, cited Toffler's The Third Wave as a formative influence on his thinking, which inspired him to write The Third Wave: An Entrepreneur's Vision of the Future in 2016. Case said that Toffler was a "real pioneer in helping people, companies and even countries lean into the future."

In 1980, Ted Turner founded CNN, which he said was inspired by Toffler's forecasting the end of the dominance of the three main television networks. Turner's company, Turner Broadcasting, published Toffler's Creating a New Civilization in 1995. Shortly after the book was released, the former Soviet president Mikhail Gorbachev hosted the Global Governance Conference in San Francisco with the theme, Toward a New Civilization, which was attended by dozens of world figures, including the Tofflers, George H. W. Bush, Margaret Thatcher, Carl Sagan, Abba Eban and Turner with his then-wife, actress Jane Fonda.

Mexican billionaire Carlos Slim was influenced by his works, and became a friend of the writer. Global marketer J.D. Power also said he was inspired by Toffler's works.

Since the 1960s, people had tried to make sense out of the effect of new technologies and social change, a problem which made Toffler's writings widely influential beyond the confines of scientific, economic, and public policy. His works and ideas have been subject to various criticisms, usually with the same argumentation used against futurology: that foreseeing the future is nigh impossible.

Techno music pioneer Juan Atkins cites Toffler's phrase "techno rebels" in The Third Wave as inspiring him to use the word "techno" to describe the musical style he helped to create Musician Curtis Mayfield released a disco song called "Future Shock," later covered in an electro version by Herbie Hancock. Science fiction author John Brunner wrote "The Shockwave Rider," from the concept of "future shock."

The nightclub Toffler, in Rotterdam, is named after him.

In the song "Victoria" by The Exponents, the protagonist's daily routine and cultural interests are described: "She's up in time to watch the soap operas, reads Cosmopolitan and Alvin Toffler".

Critical assessment
Accenture, the management consultancy firm, identified Toffler in 2002 as being among the most influential voices in business leaders, along with Bill Gates and Peter Drucker. Toffler has also been described in a Financial Times interview as the "world's most famous futurologist". In 2006, the People's Daily classed him among the 50 foreigners who shaped modern China, which one U.S. newspaper notes made him a "guru of sorts to world statesmen." Chinese Premier and General Secretary Zhao Ziyang was greatly influenced by Toffler. He convened conferences to discuss The Third Wave in the early 1980s, and in 1985 the book was the No. 2 best seller in China.

Author Mark Satin characterizes Toffler as an important early influence on radical centrist political thought.

Newt Gingrich became close to the Tofflers in the 1970s and said The Third Wave had immensely influenced his own thinking and was "one of the great seminal works of our time."

Selected awards
Toffler has received several prestigious prizes and awards, including the McKinsey Foundation Book Award for Contributions to Management Literature, Officier de L'Ordre des Arts et Lettres, and appointments, including Fellow of the American Association for the Advancement of Science and the International Institute for Strategic Studies.

In 2006, Alvin and Heidi Toffler were recipients of Brown University's Independent Award.

Personal life
Toffler was married to Heidi Toffler (born Adelaide Elizabeth Farrell), also a writer and futurist. They lived in the Bel Air section of Los Angeles, California, and previously lived in Redding, Connecticut.

The couple's only child, Karen Toffler (1954–2000), died at age 46 after more than a decade suffering from Guillain–Barré syndrome.

Alvin Toffler died in his sleep on June 27, 2016, at his home in Los Angeles. No cause of death was given. He is buried at Westwood Memorial Park.

title: Alvin Toffler


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The Amazing Spider-Man

The Amazing Spider-Man is an ongoing American superhero comic book series featuring the Marvel Comics superhero Spider-Man as its title character and main protagonist. Being in the mainstream continuity of the franchise, it was the character's first title, launching seven months after his introduction in the final issue of Amazing Fantasy. The series began publication with a March 1963 cover date and has been published nearly continuously to date over six volumes with only one significant interruption. Issues of the title currently feature an issue number within its sixth volume, as well as a "legacy" number reflecting the issue's overall number across all Amazing Spider-Man volumes. The title reached 900 issues in 2022.

The series began as a bimonthly periodical before being increased to monthly after four issues. It was the character's sole monthly headlining title until Peter Parker, the Spectacular Spider-Man launched in 1976. After 441 issues, The Amazing Spider-Man was restarted in 1999 as issue No. 1 of Volume 2. It ran for 58 issues before reverting to the title's overall issue number with #500 in 2003. The series ran essentially continuously over the first two volumes from 1963 until its landmark 700th issue at the end of 2012 when it was replaced by The Superior Spider-Man as part of the Marvel NOW! relaunch of Marvel's comic lines. The title was occasionally published biweekly during the first two volumes, and was published three times a month from 2008 to 2010. After the relaunch of Action Comics and Detective Comics, The Amazing Spider-Man briefly became the highest-numbered active American comic book.

The Amazing Spider-Man returned with volume 3 in April 2014 following the conclusion of The Superior Spider-Man story arc after 31 issues. In late 2015, the series was relaunched with a fourth volume following the 2015 Secret Wars event. After 45 years, the volume was once again relaunched as part of Marvel Legacy, returning to the overall "legacy" numbering with issue No. 789 in late 2017. Less than a year later, the series was relaunched again with a fifth volume as part of Marvel's Fresh Start. For the first time, although the issue numbers were again restarted from #1, the issues also bore the overall "legacy" issue number. A sixth volume commenced in April 2022 to celebrate Spider-Man's 60th anniversary. Since the second volume, the title has had various release schedules, including monthly and bi-weekly, among others.

Publication history
Writer-editor Stan Lee and artist and co-plotter Steve Ditko created the character of Spider-Man, and the pair produced 38 issues from March 1963 to July 1966. Ditko left after the 38th issue, while Lee remained as writer until issue 100. Since then, many writers and artists have taken over the monthly comic through the years, chronicling the adventures of Marvel's most identifiable hero.

The Amazing Spider-Man has been the character's flagship series for his first fifty years in publication, and was the only monthly series to star Spider-Man until Peter Parker, The Spectacular Spider-Man, in 1976, although 1972 saw the debut of Marvel Team-Up, with the vast majority of issues featuring Spider-Man along with a rotating cast of other Marvel characters. Most of the major characters and villains of the Spider-Man saga have been introduced in Amazing, and with few exceptions, it is where most key events in the character's history have occurred. The title was published continuously until No. 441 (Nov. 1998) when Marvel Comics relaunched it as vol. 2 No. 1 (Jan. 1999), but on Spider-Man's 40th anniversary, this new title reverted to using the numbering of the original series, beginning again with issue No. 500 (Dec. 2003) and lasting until the final issue, No. 700 (Feb. 2013).

1960s
Due to strong sales on the character's first appearance in Amazing Fantasy No. 15, Spider-Man was given his own ongoing series in March 1963. The initial years of the series, under Lee and Ditko, chronicled Spider-Man's nascent career as a masked super-human vigilante with his civilian life as hard-luck yet perpetually good-humored and well-meaning teenager Peter Parker. Peter balanced his career as Spider-Man with his job as a freelance photographer for The Daily Bugle under the bombastic editor-publisher J. Jonah Jameson to support himself and his frail Aunt May. At the same time, Peter dealt with public hostility towards Spider-Man and the antagonism of his classmates Flash Thompson and Liz Allan at Midtown High School, while embarking on a tentative, ill-fated romance with Jameson's secretary, Betty Brant.

By focusing on Parker's everyday problems, Lee and Ditko created a groundbreakingly flawed, self-doubting superhero, and the first major teenaged superhero to be a protagonist and not a sidekick. Ditko's quirky art provided a stark contrast to the more cleanly dynamic stylings of Marvel's most prominent artist, Jack Kirby, and combined with the humor and pathos of Lee's writing to lay the foundation for what became an enduring mythos.

Most of Spider-Man's key villains and supporting characters were introduced during this time. Issue No. 1 (Mar. 1963) featured the first appearances of J. Jonah Jameson and his astronaut son John Jameson, and the supervillain the Chameleon. It included the hero's first encounter with the superhero team the Fantastic Four. Issue No. 2 (May 1963) featured the first appearance of the Vulture and the Tinkerer as well as the beginning of Parker's freelance photography career at the newspaper The Daily Bugle.

The Lee-Ditko era continued to usher in a significant number of villains and supporting characters, including Doctor Octopus in No. 3 (July 1963); the Sandman and Betty Brant in No. 4 (Sept. 1963); the Lizard in No. 6 (Nov. 1963);  Living Brain in No. 8 (Jan. 1964); Electro in No. 9 (Mar. 1964);  Mysterio in No. 13 (June 1964); the Green Goblin in No. 14 (July 1964);  Kraven The Hunter in No. 15 (Aug. 1964); reporter Ned Leeds in No. 18 (Nov. 1964); and the Scorpion in No. 20 (Jan. 1965). The Molten Man was introduced in No. 28 (Sept. 1965) which also featured Parker's graduation from high school. Peter began attending Empire State University in No. 31 (Dec. 1965), which featured the first appearances of friends and classmates Gwen Stacy and Harry Osborn. Harry's father, Norman Osborn first appeared in No. 23 (April 1965) as a member of Jameson's country club but was not named nor revealed as Harry's father until No. 37 (June 1966).

One of the most celebrated issues of the Lee-Ditko run is No. 33 (Feb. 1966), the third part of the story arc "If This Be My Destiny...!", which features the dramatic scene of Spider-Man, through force of will and thoughts of family, escaping from being pinned by heavy machinery. Comics historian Les Daniels noted that "Steve Ditko squeezes every ounce of anguish out of Spider-Man's predicament, complete with visions of the uncle he failed and the aunt he has sworn to save." Peter David observed that "After his origin, this two-page sequence from Amazing Spider-Man No. 33 is perhaps the best-loved sequence from the Stan Lee/Steve Ditko era." Steve Saffel stated the "full page Ditko image from The Amazing Spider-Man No. 33 is one of the most powerful ever to appear in the series and influenced writers and artists for many years to come." and Matthew K. Manning wrote that "Ditko's illustrations for the first few pages of this Lee story included what would become one of the most iconic scenes in Spider-Man's history." The story was chosen as No. 15 in the 100 Greatest Marvels of All Time poll of Marvel's readers in 2001. Editor Robert Greenberger wrote in his introduction to the story that "These first five pages are a modern-day equivalent to Shakespeare as Parker's soliloquy sets the stage for his next action. And with dramatic pacing and storytelling, Ditko delivers one of the great sequences in all comics."

Although credited only as artist for most of his run, Ditko would eventually plot the stories as well as draw them, leaving Lee to script the dialogue. A rift between Ditko and Lee developed, and the two men were not on speaking terms long before Ditko completed his last issue, The Amazing Spider-Man No. 38 (July 1966). The exact reasons for the Ditko-Lee split have never been fully explained. Spider-Man successor artist John Romita Sr., in a 2010 deposition, recalled that Lee and Ditko "ended up not being able to work together because they disagreed on almost everything, cultural, social, historically, everything, they disagreed on characters..."

In successor penciler Romita Sr.'s first issue, No. 39 (Aug. 1966), nemesis the Green Goblin discovers Spider-Man's secret identity and reveals his own to the captive hero. Romita's Spider-Man – more polished and heroic-looking than Ditko's – became the model for two decades. The Lee-Romita era saw the introduction of such characters as Daily Bugle managing editor Robbie Robertson in No. 52 (Sept. 1967) and NYPD Captain George Stacy, father of Parker's girlfriend Gwen Stacy, in No. 56 (Jan. 1968). The most important supporting character to be introduced during the Romita era was Mary Jane Watson, who made her first full appearance in No. 42 (Nov. 1966), although she first appeared in No. 25 (June 1965) with her face obscured and had been mentioned since No. 15 (Aug. 1964). Peter David wrote in 2010 that Romita "made the definitive statement of his arrival by pulling Mary Jane out from behind the oversized potted plant [that blocked the reader's view of her face in issue no. 25] and placing her on panel in what would instantly become an iconic moment." Romita has stated that in designing Mary Jane, he "used Ann-Margret from the movie Bye Bye Birdie as a guide, using her coloring, the shape of her face, her red hair and her form-fitting short skirts."

Lee and Romita toned down the prevalent sense of antagonism in Parker's world by improving Parker's relationship with the supporting characters and having stories focused as much on the social and college lives of the characters as they did on Spider-Man's adventures. The stories became more topical, addressing issues such as civil rights, racism, prisoners' rights, the Vietnam War, and political elections.

Issue No. 50 (June 1967) introduced the highly enduring criminal mastermind the Kingpin, who would become a major force as well in the superhero series Daredevil. Other notable first appearances in the Lee-Romita era include the Rhino in No. 41 (Oct. 1966), the Shocker in No. 46 (Mar. 1967),  the Prowler in No. 78 (Nov. 1969), and the Kingpin's son, Richard Fisk, in No. 83 (Apr. 1970).

1970s
Several spin-off series debuted in the 1970s: Marvel Team-Up in 1972, and The Spectacular Spider-Man in 1976. A short-lived series titled Giant-Size Spider-Man began in July 1974 and ran six issues through 1975. Spidey Super Stories, a series aimed at children ages 6–10, ran for 57 issues from October 1974 through 1982. The flagship title's second decade took a grim turn with a story in #89-90 (Oct.-Nov. 1970) featuring the death of Captain George Stacy. This was the first Spider-Man story to be penciled by Gil Kane, who would alternate drawing duties with Romita for the next year-and-a-half and would draw several landmark issues.

One such story took place in the controversial issues #96–98 (May–July 1971). Writer-editor Lee defied the Comics Code Authority with this story, in which Parker's friend Harry Osborn, was hospitalized after over-dosing on pills. Lee wrote this story upon a request from the U. S. Department of Health, Education, and Welfare for a story about the dangers of drugs. Citing its dictum against depicting drug use, even in an anti-drug context, the CCA refused to put its seal on these issues. With the approval of Marvel publisher Martin Goodman, Lee had the comics published without the seal. The comics sold well and Marvel won praise for its socially conscious efforts. The CCA subsequently loosened the Code to permit negative depictions of drugs, among other new freedoms.

"The Six Arms Saga" of #100–102 (Sept.–Nov. 1971) introduced Morbius, the Living Vampire. The second installment was the first Amazing Spider-Man story not written by co-creator Lee, with Roy Thomas taking over writing the book for several months before Lee returned to write #105–110 (Feb.-July 1972). Lee, who was going on to become Marvel Comics' publisher, with Thomas becoming editor-in-chief, then turned writing duties over to 19-year-old Gerry Conway, who scripted the series through 1975. Romita penciled Conway's first half-dozen issues, which introduced the gangster Hammerhead in No. 113 (Oct. 1972). Kane then succeeded Romita as penciler, although Romita would continue inking Kane for a time.

Issue 121 (June 1973 by Conway-Kane-Romita) featured the death of Gwen Stacy at the hands of the Green Goblin in "The Night Gwen Stacy Died." Her demise and the Goblin's apparent death one issue later formed a story arc widely considered as the most defining in the history of Spider-Man. The aftermath of the story deepened both the characterization of Mary Jane Watson and her relationship with Parker.

In 1973 Gil Kane was succeeded by Ross Andru, whose run lasted from issue #125 (Oct. 1973) to #185 (Oct. 1978). Issue#129 (Feb. 1974) introduced the Punisher, who would become one of Marvel Comics' most popular characters. The Conway-Andru era featured the first appearances of the Man-Wolf in #124–125 (Sept.-Oct. 1973); the near-marriage of Doctor Octopus and Aunt May in #131 (Apr. 1974); Harry Osborn stepping into his father's role as the Green Goblin in #135–137 (Aug.-Oct.1974); and the original "Clone Saga", containing the introduction of Spider-Man's clone, in #147–149 (Aug.-Oct. 1975).

Archie Goodwin and Gil Kane produced the title's 150th issue (Nov. 1975) before Len Wein became writer with issue No. 151. During Wein's tenure, Harry Osborn and Liz Allen dated and became engaged; J. Jonah Jameson was introduced to his eventual second wife, Marla Madison; and Aunt May suffered a heart attack. Wein's last story on Amazing was a five-issue arc in #176–180 (Jan.-May 1978) featuring a third Green Goblin (Harry Osborn's psychiatrist, Bart Hamilton).

Marv Wolfman, Marvel's editor-in-chief from 1975 to 1976, succeeded Wein as writer and, in his first issue, #182 (July 1978), had Parker propose marriage to Watson, who refused in the following issue. Keith Pollard succeeded Andru as artist shortly afterward and, with Wolfman, introduced the likable rogue the Black Cat (Felicia Hardy) in #194 (July 1979). As a love interest for Spider-Man, the Black Cat would go on to be an important supporting character for the better part of the next decade and remain a friend and occasional lover into the 2010s.

1980s
The Amazing Spider-Man #200 (Jan. 1980) featured the return and death of the burglar who killed Spider-Man's Uncle Ben. Writer Marv Wolfman and penciler Keith Pollard both left the title by mid-year, succeeded by Dennis O'Neil, a writer known for groundbreaking 1970s work at rival DC Comics, and penciler John Romita Jr. O'Neil wrote two issues of The Amazing Spider-Man Annual which were both drawn by Frank Miller. The 1980 Annual featured a team-up with Doctor Strange while the 1981 Annual showcased a meeting with the Punisher. Roger Stern, who had written nearly 20 issues of sister title The Spectacular Spider-Man, took over Amazing with #224 (Jan. 1982). During his two years on the title, Stern augmented the backgrounds of long-established Spider-Man villains and, with Romita Jr., created the mysterious supervillain the Hobgoblin in #238–239 (Mar.–Apr. 1983). Fans engaged with the mystery of the Hobgoblin's secret identity, which continued throughout #244–245 and 249–251 (Sept.-Oct. 1983 and Feb.-April 1984). One lasting change was the reintroduction of Mary Jane Watson as a more serious, mature woman who becomes Peter's confidante after she reveals that she knows his secret identity. Stern also wrote "The Kid Who Collects Spider-Man" in The Amazing Spider-Man #248 (Jan. 1984), a story which ranks among his most popular.

By mid-1984, Tom DeFalco and Ron Frenz took over scripting and penciling. DeFalco helped establish Parker and Watson's mature relationship, laying the foundation for the characters' wedding in 1987. Notably, in #257 (Oct. 1984), Watson tells Parker that she knows he is Spider-Man, and in #259 (Dec. 1984), she reveals to Parker the extent of her troubled childhood. Other notable issues of the DeFalco-Frenz era include #252 (May 1984), the first appearance of Spider-Man's black costume, which the hero would wear almost exclusively for the next four years' worth of comics; the debut of criminal mastermind the Rose in #253 (June 1984); the revelation in #258 (Nov. 1984) that the black costume is a living being, a symbiote; and the introduction of the female mercenary Silver Sable in #265 (June 1985).

DeFalco and Frenz were both removed from The Amazing Spider-Man in 1986 by editor Jim Owsley under acrimonious circumstances. A succession of artists including Alan Kupperberg, John Romita Jr., and Alex Saviuk penciled the series from 1987 to 1988, and Owsley wrote the book for the first half of 1987, scripting the five-part "Gang War" story (#284–288) that DeFalco plotted. Former Spectacular Spider-Man writer Peter David scripted #289 (June 1987), which revealed Ned Leeds as being the Hobgoblin although this was retconned in 1996 by Roger Stern into Leeds not being the original Hobgoblin after all.

David Michelinie took over as writer in the next issue, for a story arc in #290–292 (July–Sept. 1987) that led to the marriage of Peter Parker and Mary Jane Watson in Amazing Spider-Man Annual No. 21. The "Kraven's Last Hunt" storyline by writer J.M. DeMatteis and artists Mike Zeck and Bob McLeod crossed over into The Amazing Spider-Man #293 and 294. Issue No.298 (Mar. 1988) was the first Spider-Man comic to be drawn by future industry star Todd McFarlane, the first regular artist on The Amazing Spider-Man since Frenz's departure. McFarlane revolutionized Spider-Man's look. His depiction – "Ditko-esque" poses, large eyes; wiry, contorted limbs; and messy, knotted, convoluted webbing – influenced the way virtually all subsequent artists would draw the character. McFarlane's other significant contribution to the Spider-Man canon was the design for what would become one of Spider-Man's most wildly popular antagonists, the supervillain Venom. Issue No. 299 (Apr. 1988) featured Venom's first appearance (a last-page cameo) before his first full appearance in #300 (May 1988). The latter issue featured Spider-Man reverting to his original red-and-blue costume.

Other notable issues of the Michelinie-McFarlane era include #312 (Feb. 1989), featuring the Green Goblin vs. the Hobgoblin; and #315–317 (May–July 1989), with the return of Venom. In July 2012, Todd McFarlane's original cover art for The Amazing Spider-Man No. 328 sold for a bid of $657,250, making it the most expensive American comic book art ever sold at auction.

1990s
With a civilian life as a married man, the Spider-Man of the 1990s was different from the superhero of the previous three decades. McFarlane left the title in 1990 to write and draw a new series titled simply Spider-Man. His successor, Erik Larsen, penciled the book from early 1990 to mid-1991. After issue No. 350, Larsen was succeeded by Mark Bagley, who had won the 1986 Marvel Tryout Contest and was assigned a number of low-profile penciling jobs followed by a run on New Warriors in 1990. Bagley penciled the flagship Spider-Man title from 1991 to 1996. During that time, Bagley's rendition of Spider-Man was used extensively for licensed material and merchandise.

Issues #361–363 (April–June 1992) introduced Carnage, a second symbiote nemesis for Spider-Man. The series' 30th-anniversary issue, No. 365 (Aug. 1992), was a double-sized, hologram-cover issue with the cliffhanger ending of Peter Parker's parents, long thought dead, reappearing alive. It would be close to two years before they were revealed to be impostors, who are killed in No. 388 (April 1994), scripter Michelinie's last issue. His 1987–1994 stint gave him the second-longest run as writer on the title, behind Stan Lee.

Issue No. 375 was released with a gold foil cover. There was an error affecting some issues and which are missing the majority of the foil.

With No. 389, writer J. M. DeMatteis, whose Spider-Man credits included the 1987 "Kraven's Last Hunt" story arc and a 1991–1993 run on The Spectacular Spider-Man, took over the title. From October 1994 to June 1996, Amazing stopped running stories exclusive to it, and ran installments of multi-part stories that crossed over into all the Spider-Man books. One of the few self-contained stories during this period was in No. 400 (April 1995), which featured the death of Aunt May – later revealed to have been faked (although the death still stands in the MC2 continuity). The "Clone Saga" culminated with the revelation that the Spider-Man who had appeared in the previous 20 years of comics was a clone of the real Spider-Man. This plot twist was massively unpopular with many readers, and was later reversed in the "Revelations" story arc that crossed over the Spider-Man books in late 1996.

The Clone Saga tied into a publishing gap after No. 406 (Oct. 1995), when the title was temporarily replaced by The Amazing Scarlet Spider #1–2 (Nov.-Dec. 1995), featuring Ben Reilly. The series picked up again with No. 407 (Jan. 1996), with Tom DeFalco returning as writer. Bagley completed his 5½-year run by September 1996. A succession of artists, including Ron Garney, Steve Skroce, Joe Bennett, Rafael Kayanan and John Byrne penciled the book until the final issue, No. 441 (Nov. 1998), after which Marvel rebooted the title with vol. 2, No. 1 (Jan. 1999).

Relaunch and the 2000s
Marvel began The Amazing Spider-Man relaunching the 'Amazing' comic book series with (vol. 2) #1 (Jan. 1999). Howard Mackie wrote the first 29 issues. The relaunch included the Sandman being regressed to his criminal ways and the "death" of Mary Jane, which was ultimately reversed. Other elements included the introduction of a new Spider-Woman (who was spun off into her own short-lived series) and references to John Byrne's miniseries Spider-Man: Chapter One, which was launched at the same time as the reboot. Byrne also penciled issues #1–18 (from 1999 to 2000) and wrote #13–14, John Romita Jr. took his place soon after in October 2000. Mackie's run ended with The Amazing Spider-Man Annual 2001, which saw the return of Mary Jane, who then left Parker upon reuniting with him.

With issue No. 30 (June 2001), J. Michael Straczynski took over as writer and oversaw additional storylines – most notably his lengthy "Spider-Totem" arc, which raised the issue of whether Spider-Man's powers were magic-based, rather than as the result of a radioactive spider's bite. Additionally, Straczynski resurrected the plot point of Aunt May discovering her nephew was Spider-Man, and returned Mary Jane, with the couple reuniting in The Amazing Spider-Man (vol. 2) #50. Straczynski gave Spider-Man a new profession, having Parker teach at his former high school.

Issue No. 30 began a dual numbering system, with the original series numbering (#471) returned and placed alongside the volume two number on the cover. Other longtime, rebooted Marvel Comics titles, including Fantastic Four, likewise were given the dual numbering around this time. After (vol. 2) #58 (Nov. 2003), the title reverted completely to its original numbering for issue No. 500 (Dec. 2003). Mike Deodato, Jr. penciled the series from mid-2004 until 2006.

That year Peter Parker revealed his Spider-Man identity on live television in the company-crossover storyline "Civil War", in which the superhero community is split over whether to conform to the federal government's new Superhuman Registration Act. This knowledge was erased from the world with the event of the four-part, crossover story arc, "One More Day", written partially by J. Michael Straczynski and illustrated by Joe Quesada, running through The Amazing Spider-Man #544–545 (Nov.-Dec. 2007), Friendly Neighborhood Spider-Man No. 24 (Nov. 2007) and The Sensational Spider-Man No. 41 (Dec. 2007), the final issues of those two titles. Here, the demon Mephisto makes a Faustian bargain with Parker and Mary Jane, offering to save Parker's dying Aunt May if the couple will allow their marriage to have never existed, rewriting that portion of their pasts. This story arc marked the end of Straczynski's work on the title.

Following this, Marvel made The Amazing Spider-Man the company's sole Spider-Man title, increasing its frequency of publication to three issues monthly, and inaugurating the series with a sequence of "back to basics" story arcs under the banner of "Brand New Day". Parker now exists in a changed world where he and Mary Jane had never married, and Parker has no memory of being married to her, with domino effect differences in their immediate world. The most notable of these revisions to Spider-Man continuity are the return of Harry Osborn, whose death in The Spectacular Spider-Man No. 200 (May 1993) is erased; and the reestablishment of Spider-Man's secret identity, with no one except Mary Jane able to recall that Parker is Spider-Man (although he soon reveals his secret identity to the New Avengers and the Fantastic Four). Under the banner of Brand New Day, Marvel tried to only use newly created villains instead of relying on older ones. Characters like Mister Negative and Overdrive both in Free Comic Book Day 2007 Spider-Man (July 2007), Menace in No. 549 (March 2008), Ana and Sasha Kravinoff in No. 565 (September 2008) and No. 567 (October 2008) respectively, and several more were introduced. The alternating regular writers were initially Dan Slott, Bob Gale, Marc Guggenheim, and Zeb Wells, joined by a rotation of artists that included Steve McNiven, Salvador Larroca, Phil Jimenez, Barry Kitson, Chris Bachalo, Mike McKone, Marcos Martín, and John Romita Jr. Joe Kelly, Mark Waid, Fred Van Lente and Roger Stern later joined the writing team and Paolo Rivera, Lee Weeks and Marco Checchetto the artist roster. Waid's work on the series included a meeting between Spider-Man and Stephen Colbert in The Amazing Spider-Man No. 573 (Dec. 2008). Issue No. 583 (March 2009) included a back-up story in which Spider-Man meets President Barack Obama.

2010s and temporary end of publication
Mark Waid scripted the opening of "The Gauntlet" storyline in issue No. 612 (Jan. 2010). The Gauntlet story was concluded by Grim Hunt (No. 634–637) which saw the resurrection of long-dead Spider-Man villain, Kraven the Hunter. The series became a twice-monthly title with Dan Slott as sole writer at issue No. 648 (Jan. 2011), launching the Big Time storyline. Eight additional pages were added per issue. Big Time saw major changes in Spider-Man/Peter Parker's life, Peter would start working at Horizon Labs and begin a relationship with Carlie Cooper (his first serious relationship since his marriage to Mary Jane), Mac Gargan returned as Scorpion after spending the past few years as Venom, Phil Urich would take up the mantle of Hobgoblin, and the death of J. Jonah Jameson's wife, Marla Jameson. Issues 654 and 654.1 saw the birth of Agent Venom, Flash Thompson bonded with the Venom symbiote, which would lead to Venom getting his own series Venom (volume 2). Starting in No. 659 and going to No. 665, the series built-up to the Spider-Island event which officially started in No. 666 and ended in No. 673. Ends of the Earth was the next event that ran from No. 682 through No. 687. This publishing format lasted until issue No. 700, which concluded the "Dying Wish" storyline, in which Parker and Doctor Octopus swapped bodies, and the latter taking on the mantle of Spider-Man when Parker apparently died in Doctor Octopus' body. The Amazing Spider-Man ended with this issue, with the story continuing in the new series The Superior Spider-Man. Despite The Superior Spider-Man being considered a different series to The Amazing Spider-Man, the first 33 issue run goes towards the legacy numbering of The Amazing Spider-Man acting as issues 701–733. In December 2013, the series returned for five issues, numbered 700.1 through 700.5, with the first two written by David Morrell and drawn by Klaus Janson.

2014 relaunch
In January 2014, Marvel confirmed that The Amazing Spider-Man would be relaunched on April 30, 2014, starting from issue No. 1, with Peter Parker as Spider-Man once again. The first issue of this new version of The Amazing Spider-Man was, according to Diamond Comics Distributors, the "best-selling comic book... in over a decade." Issues #1–6 were a story arc called "Lucky to be Alive", taking place immediately after "Goblin Nation", with issues No. 4 and No. 5 being a crossover with the Original Sin storyline. Issue No. 4 introduced Silk, a new heroine who was bitten by the same spider as Peter Parker. Issues #7–8 featured a team-up between Ms. Marvel and Spider-Man, and had backup stories that tied into "Edge of Spider-Verse". The next major plot arc, titled "Spider-Verse", began in Issue No. 9 and ended in No. 15, features every Spider-Man from across the dimensions being hunted by Morlun, and a team-up to stop him, with Peter Parker of Earth-616 in command of the Spider-Men's Alliance. The Amazing Spider-Man Annual No. 1 of the relaunched series was released in December 2014, featuring stories unrelated to "Spider-Verse".

The Amazing Spider-Man: Renew Your Vows
In 2015, Marvel started the universe wide Secret Wars event where the core and several other Marvel universes were combined into one big planet called Battleworld. Battleworld was divided into sections with most of them being self-contained universes. Marvel announced that several of these self-contained universes would get their own tie in series and one of them was Amazing Spider-Man: Renew Your Vows, an alternate universe where Peter Parker and Mary Jane are still married and give birth to their child Annie May Parker, written by Dan Slott. Despite the series being considered separate from the main Amazing Spider-Man series, the original 5 issue run is counted towards its legacy numbering acting as No. 752-756.

2015 relaunch
Following the 2015 Secret Wars event, a number of Spider-Man-related titles were either relaunched or created as part of the "All-New, All-Different Marvel" event. Among them, The Amazing Spider-Man was relaunched as well and primarily focused on Peter Parker continuing to run Parker Industries and becoming a successful businessman operating worldwide. It also tied with Civil War II (involving an Inhuman named Ulysses Cain who can predict possible futures), Dead No More (where Ben Reilly [the original Scarlet Spider] revealed to be revived and as one of the antagonists instead), and Secret Empire (during Hydra's reign led by a Hydra influenced Captain America/Steve Rogers, and the dismissal of Parker Industries by Peter Parker to stop Otto Octavius). Starting in September 2017, Marvel started the Marvel Legacy event which renumbered several Marvel series to their original numbering. The Amazing Spider-Man was put back to its original numbering for #789. Issues #789 through 791 focused on the aftermath of Peter destroying Parker Industries and his fall from grace. Issues #792 and 793 were part of the Venom Inc. story. Threat Level: Red was the story for the next three issues which saw Norman Osborn obtain and bond with the Carnage symbiote. Go Down Swinging saw the results of the combination of Osborn's goblin serum and Carnage symbiote creating the Red Goblin. Issue No. 801 was Dan Slott's goodbye issue.

2018 relaunch
In March 2018, it was announced that writer Nick Spencer would be writing the main semi-monthly The Amazing Spider-Man series beginning with a new No. 1, replacing long-time writer Dan Slott, as part of the Fresh Start relaunch that July. The first five-issue story arc was titled 'Back to Basics.' During the Back to Basics story, Kindred, a mysterious villain with some relation to Peter's past, was introduced, and Peter resumed his romantic relationship with Mary Jane once more. The first major story under Spencer was Hunted which ran through issues 16 through 23, the story also included four ".HU" issues for issues 16, 18, 19, and 20. The end of the story saw the death of long-running Spider-Man villain Kraven the Hunter, being replaced by his clone son, The Last Son of Kraven.

2020s
Issue 45 kicked off the Sins Rising story which saw the resurrected Sin-Eater carry out the plans of Kindred to cleanse the world of sin, particularly that of Norman Osborn. The story concluded with issue 49, issue 850 in legacy numbering, seeing Spider-Man and Green Goblin team up to defeat Sin-Eater. Last Remains started in issue 50 and concluded in issue 55, the story saw Kindred's plans come to fruition as he tormented Spider-Man. The story has also seen five ".LR" for issues 50, 51, 52, 53, and 54 which focused on The Order of the Web, a new faction of Spider-People consisting of Julia Carpenter (Madame Web), Miles Morales (Spider-Man), Gwen Stacy (Ghost-Spider), Cindy Moon (Silk), Jessica Drew (Spider-Woman), and Anya Corazon (Spider-Girl). The story also revealed that Kindred is Harry Osborn. Last Remains also received two fallout issues called Last Remains Post-Mortem.

Nick Spencer concluded his run with the Sinister War story which wrapped up in No. 74 (legacy numbering 875). The story saw several retcons to the Spider-Man mythos including that Kindred was Gabriel and Sarah Stacy all along, the fact that the Stacy twins were actually genetically engineered beings using Norman Osborn and Gwen Stacy's DNA, that the Harry Osborn that returned in Brand New Day was actually a clone, and that Norman had made a deal with Mephisto where he sold Harry's soul to the demon. The story ended with the deaths of the Harry clone, Gabriel, and Sarah and the real Harry's soul being freed from Mephisto's grasp.

After Spencer left the book, Marvel announced the "Beyond" era of Spider-Man would start in #75. The book would be moving back to the format it had during Brand New Day where it would have a rotating cast of writers including Kelly Thompson, Saladin Ahmed, Cody Ziglar, Patrick Gleason, and Zeb Wells. The book would also be released three times a month. "Beyond" would focus on Ben Reilly taking up the mantle of Spider-Man once again but backed by the Beyond corporation. Peter also falls ill and cannot be Spider-Man so he gives Ben his blessing to carry on as the main Spider-Man. However, following the conclusion of the storyline in #93, Peter has resumed active duties as Spider-Man, while Ben suffers a mental breakdown after losing his memories and becomes the villain Chasm.

2022 relaunch
In January 2022, it was announced that writer Zeb Wells and John Romita Jr. would be working on a relaunched The Amazing Spider-Man, bringing the number of volumes for the title to its sixth, with the series beginning in April 2022 as a semi-monthly publication. The relaunch encompasses both a legacy numbering of #900 as well as the 60th anniversary for the character. The relaunch took place months after a mysterious event that left Peter on bad terms with the superhero community and ended his relationship with Mary Jane. He ends up taking a job at Oscorp and begins working closely with Norman Osborn (who becomes the heroic Gold Goblin) and starts dating Black Cat. The volume's first crossover event was entitled Dark Web, with Chasm having teamed up with Madelyne Pryor to bring limbo to Earth.

It's later revealed that Benjamin Rabin, the emissary of the Mayan god of mischief Wayeb', sent Peter and Mary Jane to an alternate dimension to conduct a ceremony that would allow Wayeb to control the Earth. Peter was sent back to his Earth, while due to the alternative passage of time, Mary Jane and Paul, Rabin's son in that dimension, spent four years in the realm together and adopted two children. When Peter eventually rescued them, Mary Jane refused to part with her new family. Rabin then planned to sacrifice Mary Jane to resurrect Wayeb, but is ultimately stopped by Ms. Marvel sacrificing herself, but not before Rabin reveals that Paul and Mary Jane's kids were illusions created by him and ceased their existence. Mary Jane becomes the superheroine Jackpot using the bracelet acquired from the other dimension as Black Cat breaks up with Peter shortly before Janice Lincoln and Randy Robertson's wedding. The second crossover event was entitled Gang War, where Peter led a team of street-level superheroes to stop a massive war between New York's gangs led by Madam Masque, Tombstone, and Beetle. During an encounter with Kraven the Hunter, Peter temporarily becomes infected by Norman Osborn's sins and becomes the villainous Spider-Goblin. Eventually, Norman's sins return to him and he resumes being the Green Goblin. While fighting Spider-Man, the goblin reveals that he implanted a trigger phrase within Peters's mind that would bring forth the Spider-Goblin persona. Norman then sends Spider-Goblin to attack the Sinister Six, who he brutally defeats, but is stopped from killing them due to the intervention of Chasm.

In June 2024, it was announced that Wells would be concluding his run later that year, with Romita Jr returning for art and featuring Spider-Man in his final confrontation with Tombstone.

The 8 Deaths of Spider-Man
In July 2024, it was announced that following the conclusion of Wells' run, a 10-issue event would begin publication in the Fall called The 8 Deaths of Spider-Man. The series will be written by Joe Kelly and Justina Ireland and illustrated by Ed McGuinness and Gleb Melnikov.

Collected editions
Black-and-white
 * Essential Spider-Man Vol. 1 [#1–20, Annual #1; Amazing Fantasy #15] (ISBN 0-7851-0988-9)
 * Essential Spider-Man Vol. 2 [#21–43, Annual #2–3] (ISBN 0-7851-0989-7)
 * Essential Spider-Man Vol. 3 [#44–65, Annual #4] (ISBN 0-7851-0658-8)
 * Essential Spider-Man Vol. 4 [#66–89, Annual #5] (ISBN 0-7851-0760-6)
 * Essential Spider-Man Vol. 5 [#90–113] (ISBN 0-7851-0881-5)
 * Essential Spider-Man Vol. 6 [#114–137; Giant-Size Super Heroes #1; Giant-Size Spider-Man #1–2] (ISBN 0-7851-1365-7)
 * Essential Spider-Man Vol. 7 [#138–160, Annual #10; Giant-Size Spider-Man #4–5] (ISBN 0-7851-1879-9)
 * Essential Spider-Man Vol. 8 [#161–185, Annual #11; Giant-Size Spider-Man #6; Nova #12] (ISBN 0-7851-2500-0)
 * Essential Spider-Man Vol. 9 [#186–210, Annual #13–14; Peter Parker: Spectacular Spider-Man Annual #1] (ISBN 0-7851-3074-8)
 * Essential Spider-Man Vol. 10 [#211–230, Annual #15] (ISBN 0-7851-5747-6)
 * Essential Spider-Man Vol. 11 [#231–248, Annual #16–17] (ISBN 0-7851-6330-1)

Major story arcs
 * Marvel Visionaries: John Romita Sr. [#39–40, 42, 50, 108–109, 365; Daredevil #16–17; Untold Tales of Spider-Man #-1] (ISBN 0785117806)
 * Spider-Man: The Death of Captain Stacy [#88–90] (ISBN 0785114556)
 * Spider-Man: The Death of Gwen Stacy [#96–98, 121–122; Webspinners: Tales of Spider-Man #1] (ISBN 0785110267)
 * Spider-Man: Death of the Stacys [#88–92, 121–122] (ISBN 0785125043)
 * A New Goblin [#176–180] (ISBN 0785131175)
 * Spider-Man vs. the Black Cat [#194–195, 204–205, 226–227] (ISBN 0785115595)
 * Spider-Man: Origin of The Hobgoblin [#238–239, 244–245, 249–251, Spectacular Spider-Man (vol. 1) #85] (ISBN 0871359170)
 * Spider-Man: Birth of Venom [#252–259, 298–300, 315–317, Annual #25; Fantastic Four #274; Secret Wars #8; Web of Spider-Man #1] (ISBN 0785124985)
 * The Amazing Spider-Man: The Wedding [#290–292, Annual #2, Not Brand Echh #6] (ISBN 0871357704)
 * Spider-Man: Kraven's Last Hunt [#293–294; Web of Spider-Man #31–32; The Spectacular Spider-Man #131–132] (ISBN 0785134506)
 * Visionaries: Todd McFarlane [#298–305] (ISBN 0785108009)
 * Legends, Vol. 2: Todd McFarlane [#306–314; The Spectacular Spider-Man Annual #10] (ISBN 0785110372)
 * Legends, Vol. 3: Todd McFarlane [#315–323, 325, 328] (ISBN 0785110399)
 * Spider-Man: Venom Returns [#330–333, 344–347;Annual #25] (ISBN 0871359669)
 * Spider-Man: Carnage [#344–345, 359–363] (ISBN 0871359715)

Collections
 * Vol. 1: Coming Home [#30-35/471-476] (ISBN 0-7851-0806-8)
 * Vol. 2: Revelations [#36-39/477-480] (ISBN 0-7851-0877-7)
 * Vol. 3: Until the Stars Turn Cold [#40-45/481-486] (ISBN 0-7851-1075-5)
 * Vol. 4: The Life and Death of Spiders [#46-50/487-491] (ISBN 0-7851-1097-6)
 * Vol. 5: Unintended Consequences [#51-56/492-497] (ISBN 0-7851-1098-4)
 * Vol. 6: Happy Birthday [#57–58,500-502/498-502] (ISBN 0-7851-1343-6)
 * Vol. 7: The Book of Ezekiel [#503–508] (ISBN 0-7851-1525-0)
 * Vol. 8: Sins Past [#509–514] (ISBN 0-7851-1509-9)
 * Vol. 9: Skin Deep [#515–518] (ISBN 0-7851-1642-7)
 * Vol. 10: New Avengers [#519–524] (ISBN 0-7851-1764-4)
 * Spider-Man: The Other [#525–528; Friendly Neighborhood Spider-Man #1–4; Marvel Knights Spider-Man #19–22] (ISBN 0-7851-2188-9)
 * Civil War: The Road to Civil War [#529–531; New Avengers: Illuminati (one-shot); Fantastic Four #536–537] (ISBN 0-7851-1974-4)
 * Vol. 11: Civil War [#532–538] (ISBN 0-7851-2237-0)
 * Vol. 12: Back in Black [#539–543; Friendly Neighborhood Spider-Man #17–23, Annual #1] (ISBN 978-0-7851-2904-2)
 * Spider-Man: One More Day [#544–545; Friendly Neighborhood Spider-Man #24; The Sensational Spider-Man #41; Marvel Spotlight: Spider-Man – One More Day/Brand New Day] (ISBN 978-0-7851-3221-9)
 * Brand New Day Vol. 1 [#546–551; The Amazing Spider-Man: Swing Shift (Director's Cut); Venom Super-Special] (ISBN 078512845X)
 * Brand New Day Vol. 2 [#552–558] (ISBN 0785128468)
 * Brand New Day Vol. 3 [#559–563] (ISBN 0785132422)
 * Kraven's First Hunt [#564–567; The Amazing Spider-Man: Extra! #1 (story #2)] (ISBN 0785132430)
 * New Ways to Die [#568–573; Marvel Spotlight: Spider-Man – Brand New Day] (ISBN 0785132449)
 * Crime and Punisher [#574–577; The Amazing Spider-Man: Extra! #1 (story #1)] (ISBN 0785134174)
 * Death and Dating [#578–583, Annual #35/1] (ISBN 0785134182)
 * Election Day [#584–588; The Amazing Spider-Man: Extra! #1 (story #3), 3 (story #1); The Amazing Spider-Man Presidents' Day Special] (ISBN 0785134190)
 * 24/7 [#589–594; The Amazing Spider-Man: Extra! #2] (ISBN 0785134204)
 * American Son [#595–599; material from The Amazing Spider-Man: Extra! #3] (ISBN 0785140832)
 * Died in Your Arms Tonight [#600–601, Annual #36; material from Amazing Spider-Man Family #7] (ISBN 0785144854)
 * Red-Headed Stranger [#602–605] (ISBN 0785138692)
 * Return of the Black Cat [#606–611; material from Web of Spider-Man (vol. 2) #1] (ISBN 0785138684)
 * The Gauntlet Book 1: Electro and Sandman [#612–616; Dark Reign: The List – The Amazing Spider-Man; Web of Spider-Man (vol. 2) #2 (Electro story)] (ISBN 0785138714)
 * The Gauntlet Book 2: Rhino and Mysterio [#617–621; Web of Spider-Man (vol. 2) #3–4] (ISBN 0785138722)
 * The Gauntlet Book 3: Vulture and Morbius [#622–625; Web of Spider-Man (vol. 2) #2, 5 (Vulture story)] (ISBN 0785146121)
 * The Gauntlet Book 4: Juggernaut [#229–230, 626–629] (ISBN 0785146148)
 * The Gauntlet Book 5: Lizard [#629–633; Web of Spider-Man (vol. 2) #6] (ISBN 0785146164)
 * Spider-Man: Grim Hunt [#634–637; The Amazing Spider-Man: Extra! #3; Spider-Man: Grim Hunt – The Kraven Saga; Web of Spider-Man (vol. 2) #7] (ISBN 0785146180)
 * One Moment in Time [#638–641] (ISBN 0785146202)
 * Origin of the Species [#642–647; Spider-Man Saga; Web of Spider-Man (vol. 2) #12] (ISBN 0785146229)
 * Big Time [#648–651] (ISBN 0785146237)
 * Matters of Life and Death [#652–657, 654.1] (ISBN 0785151028)
 * Spider-Man: The Fantastic Spider-Man [#658–662] (ISBN 0785151060)
 * Spider-Man: The Return Of Anti-Venom [#663–665; Free Comic Book Day 2011: Spider-Man] (ISBN 0785151087)
 * Spider-Man: Spider-Island [#666–673; Venom (2011) #6–8, Spider-Island: Deadly Foes; Infested prologues from #659–660 and 662–665] (ISBN 0785151044)
 * Spider-Man: Flying Blind [#674–677; Daredevil #8] (ISBN 978-0-7851-6002-1)
 * Spider-Man: Trouble on the Horizon [#678–681, 679.1] (ISBN 978-0-7851-6003-8)
 * Spider-Man: Ends of the Earth [#682–687; Amazing Spider-Man: Ends of the Earth #1; Avenging Spider-Man #8] (ISBN 0785160051)
 * Spider-Man: Lizard – No Turning Back [#688–691; Untold Tales of Spider-Man #9] (ISBN 978-0-7851-6008-3)
 * Spider-Man: Danger Zone [#692–697; Avenging Spider-Man #11] (ISBN 0785160094)
 * Spider-Man: Dying Wish [#698–700] (ISBN 0-7851-6523-1)
 * The Amazing Spider-Man Omnibus Vol. 1 [#1–38, Annual #1–2; Amazing Fantasy #15; Strange Tales Annual #2; Fantastic Four Annual #1] (ISBN 0785124020)
 * The Amazing Spider-Man Omnibus Vol. 2 [#39–67, Annual #3–5; Spectacular Spider-Man #1–2] (ISBN 978-1302901806)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 1 [#1–10; Amazing Fantasy #15] (ISBN 0-7851-1256-1)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 2 [#11–19, Annual #1] (ISBN 0-7851-1264-2)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 3 [#20–30, Annual #2] (ISBN 0-7851-1188-3)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 4 [#31–40] (ISBN 0-7851-1189-1)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 5 [#41–50, Annual #3] (ISBN 0-7851-1190-5)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 6 [#51–61, Annual #4] (ISBN 0-7851-1362-2)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 7 [#62–67, Annual #5; The Spectacular Spider-Man #1–2 (magazine)] (ISBN 0-7851-1636-2)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 8 [#68–77; Marvel Super Heroes #14] (ISBN 0-7851-2074-2)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 9 [#78–87] (ISBN 978-0-7851-2462-7)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 10 [#88–99] (ISBN 978-0-7851-2932-5)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 11 [#100–109] (ISBN 978-0-7851-3507-4)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 12 [#110–120] (ISBN 978-0-7851-4214-0)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 13 [#121–131] (ISBN 0-7851-5036-6)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 14 [#132–142; Giant-Size Super-Heroes #1] (ISBN 0-7851-5975-4)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 15 [#143–155; Marvel Special Edition Treasury #1] (ISBN 0-7851-6631-9)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 16 [#156–168; Annual #10] (ISBN 0-7851-8801-0)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 17 [#169–180; Annual #11; Nova #12; Marvel Treasury Edition #14] (ISBN 0-7851-9186-0)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 18 [#181–192; Mighty Marvel Comics Calendar 1978; material From Annual #12] (ISBN 9781302494773)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 19 [#193–202; Annual #13; Peter Parker, the Spectacular Spider-Man Annual #1] (ISBN 130290339X)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 20 [#203–212; Annual #14] (ISBN 1302910256)
 * Marvel Masterworks: The Amazing Spider-Man Vol. 21 [#213–223; Annual #15] (ISBN 1302917005)
 * Amazing Spider-Man Vol. 1: (The) Parker Luck [Vol. 3 #1–6 (i.e., legacy #732–737)] (ISBN 978-0-7851-6676-4)
 * Amazing Spider-Man Vol. 2: Spider-Verse Prelude [#7–8 (i.e., legacy #738–739); Superior Spider-Man #32–33; Free Comic Book Day 2014 (Guardians of the Galaxy) #1] (ISBN 978-0-7851-8798-1)
 * Amazing Spider-Man Vol. 3: Spider-Verse [#9–15 (i.e., legacy #740–746)] (ISBN 978-0-7851-9234-3)
 * Amazing Spider-Man Vol. 4: Graveyard Shift [#16–18 (i.e., legacy #747–749); Annual 2015] (ISBN 978-0-7851-9338-8)
 * Amazing Spider-Man Vol. 5: Spiral [#16.1–20.1(i.e., legacy #750–751)] (ISBN 978-0-7851-9316-6)
 * Amazing Spider-Man: Renew Your Vows [#1–5 (i.e., legacy #752–756)]
 * Amazing Spider-Man Worldwide Vol. 1 [Vol. 4 #1–5]
 * Amazing Spider-Man Worldwide Vol. 2 [#6–11]
 * Amazing Spider-Man Worldwide Vol. 3 [#12–15]
 * Amazing Spider-Man Worldwide Vol. 4 [#16–19]
 * Amazing Spider-Man Worldwide Vol. 5 [#20–24, Annual #1]
 * Amazing Spider-Man Worldwide Vol. 6 [#25–28]
 * Amazing Spider-Man Worldwide Vol. 7 [#29–32 (i.e., legacy #785–788), #789–791]
 * Amazing Spider-Man: Venom Inc. [Venom Inc. Alpha, Venom Inc. Omega, #792–793, Venom #159–160]
 * Amazing Spider-Man Worldwide Vol. 8 [#794–796, Annual]
 * Amazing Spider-Man Worldwide Vol. 9 [#797–801]
 * Amazing Spider-Man: Clone Conspiracy [#19-24; The Clone Conspiracy #1-5; The Clone Conspiracy: Omega; Silk #14-17; Prowler #1-5]
 * Amazing Spider-Man: Red Goblin [#794–801]
 * Amazing Spider-Man Vol. 1: Back to Basics [#1–5, FCBD 2018: Amazing Spider-Man]
 * Amazing Spider-Man Vol. 2: Friends and Foes [#6–10]
 * Amazing Spider-Man Vol. 3: Lifetime Achievement [#11–15]
 * Amazing Spider-Man Vol. 4: Hunted [#16–23, #16.1, #18.1–20.1]
 * Amazing Spider-Man Vol. 5: Behind the Scenes [#24–28]
 * Amazing Spider-Man Vol. 6: Absolute Carnage [#29–31]
 * Amazing Spider-Man Vol. 7: 2099 [#32–36]
 * Amazing Spider-Man Vol. 8: Threats & Menaces [#37–43]
 * Amazing Spider-Man Vol. 9: Sins Rising [#44–47, Amazing Spider Man: Sins Rising #1]
 * Amazing Spider-Man Vol. 10: Green Goblin Returns [#48–49, Amazing Spider-Man: The Sins of Norman Osborn #1, FCBD 2020: Spider-Man/Venom]
 * Amazing Spider-Man Vol. 11: Last Remains [#50–55]
 * Amazing Spider-Man: Last Remains Companion [#50.1–54.1]
 * Amazing Spider-Man Vol. 12: Shattered Web [#56–60]
 * Amazing Spider-Man Vol. 13: King's Ransom [#61–65, Giant Size Amazing Spider-Man: King's Ransom #1]
 * Amazing Spider-Man Vol. 14: Chameleon Conspiracy [#66–69, Giant Size Amazing Spider-Man: Chameleon Conspiracy #1]
 * Amazing Spider-Man Vol. 15: What Cost Victory? [#70–74]
 * Amazing Spider-Man: Beyond Vol. 1 [#75–80, 78.BEY]
 * Amazing Spider-Man: Beyond Vol. 2 [#81-85, 80.BEY]
 * Amazing Spider-Man: Beyond Vol. 3 [#86-88, 88.BEY]
 * Amazing Spider-Man: Beyond Vol. 4 [#89-93, 92.BEY]
 * Amazing Spider-Man Vol. 1: World Without Love [#1-5]
 * Amazing Spider-Man Vol. 2: The New Sinister [#6-8]
 * Amazing Spider-Man Vol. 3: Hobgoblin [#9-14]
 * Amazing Spider-Man Vol. 4: Dark Web [#15-18, Dark Web #1, Dark Web: Omega #1]
 * Amazing Spider-Man Vol. 5: Dead Language Part 1 [#19-23]
 * Amazing Spider-Man Vol. 6: Dead Language Part 2 [#24-26, Annual, Fallen Friend #1]
 * Amazing Spider-Man Vol. 7: Armed and Dangerous [#27-31, FCBD 2023: Spider-Man/Venom]

title: The Amazing Spider-Man