One of my favorite not-much-talked about analysis books is "A Radical Approach to Real Analysis" by Bressoud. Must read if you enjoy reading about the history of mathematics and famous mathematicians. A lot of people here recommend Rudin or Royden, but I have seen many people become turned off to the whole field of analysis because of how terse and user-unfriendly those are. In that sense, ARTRA is the polar opposite. The follow-up, A Radical Approach to Lebesgue's Theory of Integration, is also superb.