Who writes about Postmodernism, anyway?
The one and only unignorable book on this subject is Fredric Jameson’s Postmodernism, or, the Cultural Logic of Late Capitalism. It’s a masterpiece of criticism and of thought, but it will be very slow and tough going for you (as it is for everyone), and not sharing Jameson’s massive breadth of reading (as few of us do) means you’ll miss some references. Read it anyway, even at a rate of one page per day carefully considered.
I heartily second the McHale recommendation; a broad, accessible introduction to notions of postmodernism (beyond literature) is The Postmodern Turn by Kellner and Best. As for Jameson, he’s one of the heavyweights in modern literary theory of a certain stripe and that’s a keystone text, deserving of classic status. But his writing is an acquired taste; I nearly died getting through The Political Unconscious as an undergrad (interesting book though).