Ok I've done an introductary course in analysis using the first 2/3 of Parzynski and Zipse - Introduction to Mathematical Analysis. This (I think) is about equivalent to Rudin up and including chap 7 (series of functions). I probably won't have time to take any more classes in mathematics as I'm more of a theoretical physicist, but I'd still try to advance my knowledge in analysis a bit on my own. The problem is I don't know in which direction I should continue. So far I'm considering one of the following options: 1) Fleming - Functions of Several Variables 2) Kreyzig - Introductory Functional analysis 3) Spivak - Calculus on Manifolds The criteria is that it can't be too big a step up as I'm not a mathematician and I'll be studying on my own. Kreyzig looks very nice from that aspect, while Spivak seems scary. Anybody has any suggestions?