本书共7章，主要包括集合论与巴拿赫丛、局部紧群，代数表示理论、局部凸表示与巴拿赫代数、C*-代数及其*-表示，*-表示空间的拓扑学，Stone-Weierstrass定理、希尔伯特空间中的无界算子、阿贝尔群和交换巴拿赫*-代数丛等内容。

Preface
Introduction to Volume 1 (Chapters I to VII)
Chapter I. Preliminaries
1. Logical, Set and Functional Notation
2. Numerical Notation
3. Topology
4. Algebra
5. Seminorms, Normed Spaces, Normed Algebras
6. Hilbert Spaces
7. Exercises for Chapter I
Notes and Remarks
Chapter II. Integration Theory and Banaeh Bundles
1. δ-Rings, Measures, and Measurable Functions
2. Integration of Complex Functions
3. The Outsize ψep Spaces
4. Local Measurability Structures
5. Integration of Functions with Values in a Banach Space
6. Integration of Functions with Values in a Locally Convex Space
7. The Radon-Nikodym Theorem and Related Topics
8. Measures on Locally Compact Hausdorff Spaces
9. Product Measures and Fubini's Theorem
10. Measure Transformations
11. Projection-Valued Measures and Spectral Integrals
12. The Analogue of the Riesz Theorem for Projection-Valued Measures
13. Banach Bundles
14. Banach Bundles over Locally Compact Base Spaces
15. Integration in Banach Bundles over Locally Compact Spaces
16. Fubini Theorems for Banach Bundles
17. Exercises for Chapter II
Notes and Remarks
Chapter III. Locally Compact Groups
1. Topological Groups and Subgroups
2. Quotient Spaces and Homomorphisms
3. Topological Transformation Spaces
4. Direct and Semidirect Products
5. Group Extensions
6. Topological Fields
7. Haar Measure
8. The Modular Function
9. Examples of Haar Measure and the Modular Function
10. Convolution and Involution of Measures on G
11. Convolution of functions, the L#1 group algebra
12. Relations between Measure and Topology on G
13. Invariant Measures on Coset Spaces
14. Quasi-Invariant Measures on Coset Spaces
15. Exercises for Chapter III
Notes and Remarks
Chapter IV. Algebraic Representation Theory
1. Fundamental Definitions
2. Complete Reducibility and Multiplicity for Operator Sets
3. Representations of Groups and Algebras
4. The Extended Jacobson Density Theorem
5. Finite-dimensional Semisimple Algebras
6. Application to Finite Groups
7. The Complex Field and *-Algebras
8. Exercises for Chapter IV
Notes and Remarks
Chapter V. Locally Convex Representations and Banaeh Algebras
1. Locally Convex Representations; Fundamental Definitions
2. Extending Locally Convex Representations of Two-Sided Ideals
3. The Naimark Relation
4. Elementary Remarks on Normed Algebras; Examples
5. The Spectrum
6. Spectra in Banach Algebras, Mazur's Theorem, Gelfand's Theorem
7. Commutative Banach Algebras
8. Function Algebras and ψ0(S)
9. Factorization in Banach Algebras
10. Exercises for Chapter V
Notes and Remarks
Chapter VI. C*-Algebras and Their *-Representations
1. *-Algebras; Elementary Remarks and Examples
2. Symmetric *-Algebras
3. C*-Algebras
4. Commutative C*-Algebras
5. Spectra in Subalgebras of C*-Algebras
6. The Functional Calculus in C*-Algebras
7. Positive Elements and Symmetry of C*-Algebras
8. Approximate Units in a C*-Algebra; Applications to Ideals and Quotients
9. Elementary Remarks on *-Representations
10. The C*-Completion of a Banach *-Algebra; Stone's Theorem
11. The Spectral Theory of Bounded Normal Operators
12. The Spectral Theory of Unbounded Normal Operators
13. Polar Decomposition of Operators; Mackey's Form of Schur's Lemma
14. A Criterion for Irreducibility; Discrete Multiplicity Theory
15. Compact Operators and Hilbert-Schmidt Operators
16. The Sturm-Liouville Theory
17. Inductive Limits of C*-Algebras
18. Positive Functionals
19. Positive Functionals and *-Representations
20. Indecomposable Positive Functionals and Irreducible *-Representations
21. Positive Functionals on Commutative *-Algebras; the Generalized Bochner and Plancherel Theorems
22. The Existence of Positive Functionals and *-Representations of C*-Algebras; the Gelfand Naimark Theorem