Dear Physics Forum personnel, I am a undergraduate student with math and CS major who is currently taking an introductory analysis course called MATH 521 (Rudin-PMA). On the next semester, I will be taking the course called MATH 522, which is a sequel to 521. My impression is that 522 will be an analysis on manifolds, so I have been browsing books like Spivak, Munkres, Hubbard/Hubbard, Fleming, etc. However, I learned today that the course outline of 522 is deviated from my initial impression of it being the multivariable-analysis course. According to the course outline (URL is below), it seems the topics touch more or less the real analysis and topology. The official textbook is Rudin-PMA, but I do not think that book covers many topics for the 522. Could you suggest me some books dedicated to 522? URL: https://www.math.wisc.edu/sites/default/files/521-522_0_1.pdf (very last page) URL: http://www.math.wisc.edu/~beichman/Syllabus522F14.pdf [Broken] (slight deviation) URL: https://www.math.wisc.edu/~seeger/522/syl.pdf (another deviated syllabus) Should I get the books on real and functional analysis like Rudin-RCA, Stein/Sharkachi, Kolmogorov, Simmons, Lang-RFA?