This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.

• Preface to the Fourth Edition
• Preface to the Second and Third Editions
• Preface to the First Edition
• The Logical Dependence of the Contents
• Contents
• Chapter 1. Basic Topics and Examples
• Chapter 2. The Basic Representation Theory of Compact Groups
• Chapter 3. The Ideas of Peter and Weyl
• Chapter 4. Characters
• Chapter 5. Linear Lie Groups
• Chapter 6. Compact Lie Groups
• Chapter 7. Duality of Abelian Topological Groups
• Chapter 8. Compact Abelian Groups
• Chapter 9. The Structure of Compact Groups
• Chapter 10. Compact Group Actions
• Chapter 11. The Structure of Free Compact Groups
• Chapter 12. Cardinal Invariants of Compact Groups
• Appendix 1. Abelian Groups
• Appendix 2. Covering Spaces and Groups
• Appendix 3. A Primer of Category Theory
• Appendix 4. Selected Results on Topology and Topological Groups
• Appendix 5. Measures on Compact Groups
• Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups
• Appendix 7. Weakly Complete Vector Spaces and Algebras
• References
• Index of Symbols
• Index