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Apr 12, 2010 at 11:02 comment added cheater I have split out this answer into separate ones for each book - John Stillwell's comment was originally for all of them in one answer.
Apr 11, 2010 at 21:54 history edited cheater CC BY-SA 2.5
split answer to have one resource per answer.
Apr 11, 2010 at 14:04 comment added cheater Another book I almost included in this list: Dieudonne - Treatise on Analysis Haven't included it because there's a (discontinued) translation to English from the 70s. Huge book: some editions have more than ten tomes. Huge amount of knowledge. All organized nicely in an easily understood structure, with hints on how to most quickly arrive at a certain theorem. Read it all and you'll know analysis the way a PhD student should. Dieudonne is the (often forgotten) co-author of Grothendieck's Éléments de géométrie algébrique - if one likes EGA, they'll enjoy this book as well.
Apr 9, 2010 at 22:11 comment added John Stillwell Very interesting suggestions! While on the subject of "more linear algebra than you can shake a stick at", I'd like to mention Brieskorn's Lineare Algebra und Analytische Geometrie, volumes I and II (Vieweg 1983, 1985). This is the most fascinating linear algebra book I've ever seen, but very long and rambling.
Apr 9, 2010 at 20:01 history answered cheater CC BY-SA 2.5