Chomskyan linguistics, beginning with his Syntactic Structures, a distillation of his Logical Structure of Linguistic Theory (1955, 75), challenges structural linguistics and introduces transformational grammar. This approach takes utterances (sequences of words) to have a syntax characterized by a formal grammar; in particular, a context-free grammar extended with transformational rules.
Perhaps his most influential and time-tested contribution to the field is the claim that modeling knowledge of language using a formal grammar accounts for the "productivity" or "creativity" of language. In other words, a formal grammar of a language can explain the ability of a hearer-speaker to produce and interpret an infinite number of utterances, including novel ones, with a limited set of grammatical rules and a finite set of terms. He has always acknowledged his debt to Pāṇini for his modern notion of an explicit generative grammar, although it is also related to rationalist ideas of a priori knowledge.
It is a popular misconception that Chomsky proved that language is entirely innate, and that he discovered a "universal grammar" (UG). In fact, Chomsky simply observed that while a human baby and a kitten are both capable of inductive reasoning, if they are exposed to exactly the same linguistic data, the human child will always acquire the ability to understand and produce language, while the kitten will never acquire either ability. Chomsky labeled whatever the relevant capacity the human has that the cat lacks the "language acquisition device" (LAD) and suggested that one of the tasks for linguistics should be to figure out what the LAD is and what constraints it puts on the range of possible human languages. The universal features that would result from these constraints are often termed "universal grammar" or UG.
The Principles and Parameters approach (P&P) -- developed in his Pisa 1979 Lectures, later published as Lectures on Government and Binding (LGB) -- makes strong claims regarding universal grammar: that the grammatical principles underlying languages are innate and fixed, and the differences among the world's languages can be characterized in terms of parameter settings in the brain (such as the pro-drop parameter, which indicates whether an explicit subject is always required, as in English, or can be optionally dropped, as in Spanish), which are often likened to switches. (Hence the term principles and parameters, often given to this approach.) In this view, a child learning a language need only acquire the necessary lexical items (words, grammatical morphemes, and idioms), and determine the appropriate parameter settings, which can be done based on a few key examples.
Proponents of this view argue that the pace at which children learn languages is inexplicably rapid, unless children have an innate ability to learn languages. The similar steps followed by children all across the world when learning languages, and the fact that children make certain characteristic errors as they learn their first language, whereas other seemingly logical kinds of errors never occur (and, according to Chomsky, should be attested if a purely general, rather than language-specific, learning mechanism were being employed), are also pointed to as indications of innateness.
More recently, in his Minimalist Program (1995), while retaining the core concept of "principles and parameters," Chomsky attempts a major overhaul of the linguistic machinery involved in the LGB model, stripping from it all but the barest necessary elements, while advocating a general approach to the architecture of the human language faculty that emphasizes principles of economy and optimal design, reverting to a derivational approach to generation, in contrast with the largely representational approach of classic P&P.
Chomsky's ideas have had a strong influence on researchers of language acquisition in children, though many researchers in this area such as Elizabeth Bates and Michael Tomasello argue very strongly against Chomsky's theories, and instead advocate emergentist or connectionist theories, explaining language with a number of general processing mechanisms in the brain that interact with the extensive and complex social environment in which language is used and learned.
His best-known work in phonology is The Sound Pattern of English (1968), written with Morris Halle (and often known as simply SPE). This work has had a great significance for the development in the field. While phonological theory has since moved beyond "SPE phonology" in many important respects, the SPE system is considered the precursor of some of the most influential phonological theories today, including autosegmental phonology, lexical phonology and optimality theory. Chomsky no longer publishes on phonology.