Noam Chomsky:

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Chomsky's hypothesis is that sound and meaning are mediated by syntactic representations. A universal grammar, an innate property of the human mind, defines what is a possible grammar, and therefore a possible language.
The government-binding theory puts constraints on which features can occur in the same rule, so that grammatical information is modularized and localized (e.g., the "projection principle" states that lexical properties must be satisfied in the same way at all levels of syntactic representation). This process of constraining minimizes the effort required to learn a grammar (it limits possible rule applications).
Universal principles of grammar limit language-specific options to a (small) set of "parameters".
The lexicon is the repository of lexical information that cannot be predicted from the universal principlesor from choices of parameters.
The final level of syntactic derivation, that of "logical form", must meet the "theta criterion" (every theta role must be uniquely assigned).
Every sentence has a quadruple structure: the D-structure is generated by phrase-structure rules, the S-structure is obtained from the D-structure by applying transformational rules, the P-structure (a phonetical structure) and a logical form (a semantic component, a first-order logical representation of the semantics of a natural-language sentence).
An anaphor is bound in its local domain. A pronominal is free in its local domain. An r-expression (non-anaphoric and non-pronominal) is free.
His 1970 X-bar theory eliminated the distinction between features and categories, and reduced every expression to a set of features. This way verbs and nouns (e.g., "destroy" and "destruction") are related in virtue of the features they share. The X-bar theory was made possible by the separation of the lexicon from the phrase structure rules (i.e., from the computation).
The projection principle, the theta theory and the X-bar theory compose the structure-building tools of the theory of government and binding.
A universal grammar should include a number of interacting subsystems to deal with specific problems, such as the relations of anaphors to their precedents (theory of binding) and the relations between the head of a construction and categories dependent on it (theory of government). Other subsystems involve determining thematic roles, assigning abstract cases, posing locality conditions.