PreliminariesTopological spacesA first look at Hilbert spaces and Fourier seriesMeasure theoryConvexity and Banach spacesTempered distributions and the Fourier transformBonus chapter: Probability basicsBonus chapter: Hausdorff measure and dimensionBonus chapter: Inductive limits and ordinary distributionsBibliographySymbol indexSubject indexAuthor indexIndex of capsule biographies.

A Comprehensive Course in Analysis by Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Part 1 is devoted to real analysis.