Lacan: Some Key Concepts
1	We only come to know ourselves as a self, as an independent entity distinct from others and the world, through language and other systems of representation. But because of the nature of representation and subjectivity, this self-recognition involves a series of losses, an absence or lack inscribed in the heart of subjectivity.
2	Language precedes and determines subjectivity. Language is not a function of our identities and desires so much as our identities and desires are functions of language.
3	Language genders our identities. This is one of our first losses: a fall from pre-gendered wholeness into sexual difference ("it's a boy!").
4	Lacan's mirror stage can be understood as a metaphor for subjectivity. In the mirror stage, the fragmented infant identifies with and desires to be like an image of wholeness (the image in the mirror, the "I" or subject position that implies a coherent, unified, subjectivity). But while images of wholeness give us an image of ourselves as distinct from the world, they never align with us perfectly. There is an inevitable, structural, gap between the truth of fragmentation (a body that constantly takes in and spews out matter, a consciousness riven by representations) and images of self-identity and wholeness.
5	In the Oedipal Complex, as Lacan casts it, the subject passes from a register of imaginary fusions with the world and with others (The Imaginary) into language (the Symbolic). Lacan almost describes this as a fall from Edenic presence and fusion into a post-lapsarian world of subject and object, division and desire.
6	Lacan's notion of desire is, at its heart, a desire for wholeness--a "hole in the self" that the subject attempts to close through an endless, metonymic chain of supplements: the perfect car, the perfect boyfriend, a tenure track job, etc. But as soon as one supplement is acquired, desire moves onto something else. Desire is a (representational) itch that can never truly be scratched.
	Special Bonus: The Phallus! While all of them agree it's important, some critics say the term "the Phallus" has as many as eight meanings and as few as one meaning in Lacan's work. One thing everyone pretty much agrees on, though, is that Lacan tries to maintain a distinction between the Phallus as a signifier privileged male attributes, and the penis, as a spongy little organ that can rarely (if ever) live up the Phallus's inflated claims. Anyway, looking at the gap between masculinity as it is "supposed" to be (Arnold Schwarzenegger) and as it's experienced is a fruitful area of analysis.
	Other Developments Giles Deleuze and Felix Guattari mount a powerful critique of the notion that desire is lack and that the Oedipus Complex determines subjectivity, sexual difference, and just about anything else in their 1972 book Anti-Oedipus: Capitalism and Schizophrenia. Among other things, the book is a wild, wild read. In her book, Gender Trouble, Judith Butler agrees with Lacan and French Feminists that language is patriarchal, but critiques the idea that this has determinative effects. In her words: "the law [of patriarchal language] is not deterministic, but bumbling; it prepares the ground for the insurrections against it."