Chapter 1. Preliminaries
Chapter 2. Operator basics
Chapter 3. Compact operators, mainly on a Hilbert space
Chapter 4. Orthogonal polynomials
Chapter 5. The spectral theorem
Chapter 6. Banach algebras
Chapter 7. Bonus chapter: Unbounded self-adjoint operators

A Comprehensive Course in Analysis by Poincaré Prize winner 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. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.

Part 4 focuses on operator theory, especially on a Hilbert space. Central topics are the spectral theorem, the theory of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. There is also an introduction to the theory of orthogonal polynomials and a long chapter on Banach algebras, including the commutative and non-commutative Gel'fand-Naimark theorems and Fourier analysis on general locally compact abelian groups. --- summary provided by publisher