The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view.

1 General Topology.- 1.1. Ordered Sets.- 1.2. Topology.- 1.3. Convergence.- 1.4. Continuity.- 1.5. Separation.- 1.6. Compactness.- 1.7. Local Compactness.- 2 Banach Spaces.- 2.1. Normed Spaces.- 2.2. Category.- 2.3. Dual Spaces.- 2.4. Seminormed Spaces.- 2.5. w*-Compactness.- 3 Hilbert Spaces.- 3.1. Inner Products.- 3.2. Operators on Hilbert Space.- 3.3. Compact Operators.- 3.4. The Trace.- 4 Spectral Theory.- 4.1. Banach Algebras.- 4.2. The Gelfand Transform.- 4.3. Function Algebras.- 4.4. The Spectral Theorem, I.- 4.5. The Spectral Theorem, II.- 4.6. Operator Algebra.- 4.7. Maximal Commutative Algebras.- 5 Unbounded Operators.- 5.1. Domains, Extensions, and Graphs.- 5.2. The Cayley Transform.- 5.3. Unlimited Spectral Theory.- 6 Integration Theory.- 6.1. Radon Integrals.- 6.2. Measurability.- 6.3. Measures.- 6.4. LP-Aspaces.- 6.5. Duality Theory.- 6.6. Product Integrals.- List of Symbols.

G.K. Pedersen Analysis Now "The writing is clear and precise, but has an informal and humorous touch which enlivens the material. One of the strengths of the book is the excellent set of problems, which accompany the text."—MATHEMATICAL REVIEWS