Jacques Derrida was born in Algiers in 1930. He has studied and taught in both Paris and the United States. Derrida is often regarded as the father of post structuralism or deconstructionism. 

His books include Writing and Difference and Of Grammatology. Of Grammatology was translated into English by Gayatri Chakravorty Spivak.

Derrida, and his deconstructionist counterparts, attempt to demystify the lingering epistemologies of the Enlightenment and the construction of Western thought in general. This demystification involves breaking down the arbitrary categories that structural sociologists, influenced by Western science and philosophy, have used in the past to understand the world. Examples of these categories include, but are not limited to, "self/other" (from Hegel), "bourgeoisie/proletariat" (Marx), and "mind/body". Derrida sees these dichotomous categories as problematic because meaning is lost when philosophers and scientists try to distill ideas down into fixed concepts.

The very language that is used to discuss structuralism and deconstructionalism is  flawed, according to Derrida,  because of many intrinsic contradictions. Using words like “sturcture,” “sign,” and “signifier” all keep certain processes and phenomenons/“events” in boxes with defined signified meanings. These meanings have been constructed by use of a dominant ideology and are used in ways that assume their meanings instead of exploring/deconstructing what those terms signify.

Derrida critiques structualism and the idea of a “law of cental precence” . Derrida finds that too many Western thinkers try to find a unified center in any given concept or social system when in reality there are heterogeneous and complex relationships occurring that cannot be simplified into a particular, identifiable, and categorizable structure. Structuralism is also a contradictory epistemology in Derrida's mind because  it assumes that the center is somehow both inside and outside of the structures it produces. This center is as true to its original definition as it can be and other meanings are never substituted. However, sturcturalists use different words and phrases, metaphors, to talk about the system, therefore a number of substitutions occur, and its representation can become skewed.

Derrida brings up contradiction in deconstruction, too, on the basis of language:

“…all these deconstructive discourses and all their analouges are trapped in a kind of circle. This circle is unique. It describes the form of the realtion between the history of metaphysics and the deconstruction of the hiostry of metaphysics…. We have no language—no syntax and no lexicon—which is foreign to this history; we can pronounce not a single destructive proposition which has not already had to slip into the form, the logic, and the implicit postulations of precisely what it seeks to contest.” 

So, deconstructionists are dependent on a system of language, a structure, to discuss the structures that they want to critique. Communicating ideas depends inherently on a mutually understood system, i.e. language. Each word involved in this language has a set of implied meanings that are supposedly communally known/felt/understood. What Derrida meant is that when speaking, noone can assume that our ways of communicating always have shared meanings, because how are we supposed to know that they do? And, how can they?

According to Derrida, post-structuralist thought is based on discourse analysis. Understanding the world through discourse represents a decentralized way of looking at the interworkings of the world because discourses cannot exist outside of themselves. 

Foucault adopts Derrida’s discourse theory.

Foucault's analysis of the diffusion of power throughout society and his idea that 

power relationships permeate the idea of truth and knowledge itself can is very similar to Derrida’s work. 

Some critiques of Derrida are that he uses, in Foucault's words, "obscurantism terrorism" in his writing, which basically refers to the fact that his writing it almost unreadable (some would argue entirely so) because of it's theoretical and rhetorical density and obscurity.