I am looking now to self-study (real) Analysis as it is one of the main pillars of modern mathematics, and a very useful requisite to many other complex theories and topics (e.g. topology, algebraic geometry, etc.) - and of course being interested in it! I have already studied Abstract Algebra (studied from Serge Lang Undergraduate Algebra), Calculus 1-3 (so therefore including multivariable and vector calculus), and Linear Algebra (with formal proofs). I find myself now quite comfortable with formal proofs, although apart from calculus I have no previous experience with Analysis. As I am self-studying, a good solution set is imperative also. I was thinking maybe of Rudin, Kolmogorov, Serge Lang Undergraduate Analysis, etc.? Anyway, all recommendations of books for Analysis very much appreciated. Thank you
closed as primarily opinion-based by Thomas, Shailesh, JonMark Perry, Xander Henderson, Robert Soupe Sep 4 '17 at 5:30
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Big fan of Strichartz' Way of Analysis and Abbott's Understanding Analysis for self-study.