Derrida began with continental philosophy (Husserl, Heidegger) and then moved to a critique of linguistics, philosophy of language, and the metaphysics of language as a system of signs.

Critique of linguistics and main traditions of Western philosophy: Language creates a series of metaphysical illusions that certain philosophies and ideologies have exploited (religions, totalitarian governments) and turned into unquestioned, permanent, natural categories.

"Structure, Sign, and Play:" questions the idea of structure in structuralism:

• Belief in center and structure seemed unquestioned
• Derrida decenters the idea of structure and sign system
• Structure of inner and outer (inside content/outside form), speech and writing questioned
• Derrida says there is no there there, centers are an illusion, a mirage of language.
• No secure, transcendental signified (God, truth, being, etc.) when signs and signification are rigorously examined.
• Totalizing systems are thus related to totalitarianism and imperialisms (a political move within deconstructive theory)
• Signs set up play of significations in chains of supplements and deferrals.
  • "Play" here means slippage, vacillation, substitution, supplements (not random or without rule): meaning is generated within a sign system by a "play" of supplements (chain of interpretations or substitutions of signs)

Of Grammatology

Premises: culture and thought are based on a set of unquestioned oppositions, a system of differences, differentiations, categories that mutually entail one another. The oppositions are taken as given, natural, obvious, what goes without saying. The sign structure of language, especially writing--externalized or stored or deferred language--is a model for deconstructing the symbolic code that presents itself as obvious and given rather than constructed.

• The mutual entailment in our binary structures is obscured in ideologies and a cultural hierarchizing of the binary tandem, emphasizing one part of the binary structure as higher than the other rather than seeing them as mutually necessary to the existence of the structure per se.
  
• Deconstruction is the procedure of thinking against the obvious, exposing that what seems natural and given in our meaning systems is in fact constructed (structured), that is, not natural, and embedded in and sustained by cultural systems of belief and ideology.

• Notice how writing and speech can occupy the same side of the binary opposition.
  
• Speech is everywhere saturated, inscribed, with the properties of writing: all language is a form of "arche writing," marked by temporality: a succession of signs in time, spacing between signs, differences, absences not presences.
  
• Meanings, illusion of stability, through "trace". Deconstruction cancels the search or need for origin, since there is no grounding origin for language or signs.
  
• Signs function only in a network, chains of signs, traces of differential connections in the network, differences and deferrals.

Useful overview of Key Terms with Bibliography here.