This is one of the classic books in analysis. It provides a critical transition from elementary calculus to measure theory. More importantly, it introduces the reader to some of the abstract thinking that pervades modern analysis and advanced finance. The exposition is so clear and well planned that this book is perfect for self study.

Topics include: point set topology, limits and continuity, derivatives, Riemann-Stieltjes and Lebesgue integrals, basic measure theory, infinite series and products, sequences of functions, Fourier analysis and much more. If you want to improve your mathematical skills to a level where you can study advanced topics in derivatives pricing and market theory, this book is a critical first step. I cannot recommend it highly enough.