Barry Simon, I.B.M. Professor of Mathematics and Theoretical Physics at the California Institute of Technology, is the author of several books, including such classics as Methods of Mathematical Physics (with M. Reed) and Functional Integration and Quantum Physics. This new book, based on courses given at Princeton, Caltech, ETH-Zurich, and other universities, is an introductory textbook on representation theory. According to the author, "Two facets distinguish my approach. First, this book is relatively elementary, and second, while the bulk of the books on the subject is written from the point of view of an algebraist or a geometer, this book is written with an analytical flavor".

The exposition in the book centers around the study of representation of certain concrete classes of groups, including permutation groups and compact semisimple Lie groups. It culminates in the complete proof of the Weyl character formula for representations of compact Lie groups and the Frobenius formula for characters of permutation groups. Extremely well tailored both for a one-year course in representation theory and for independent study, this book is an excellent introduction to the subject which, according to the author, is unique in having "so much innate beauty so close to the surface".

• Preface
• Chapters VIII, VII, and III
• Fundamentals of group represetnations (Chapter 2)
• Introduction
• Groups and counting principles (Chapter I)
• Fundamentals of group representations (Chapter II)
• Abstract theory of representations of finite groups (Chapter III)
• Representations of concrete finite groups. I: Abelian and Clifford groups (Chapter IV)
• Representations of concrete finite groups. II: Semidirect products and induced representations (Chapter V)
• Concrete representations of finite groups. III: The symmetric groups (Chapter VI)
• Compact groups (Chapter VII)
• The structure of compact semisimple groups (Chapter VIII)
• The representations of compact semisimple groups (Chapter IX)
• Multilinear algebra (Appendix A)
• The analysis of self-adjoint Hilbert-Schmidt operators (Appendix B)
• Bibliography
• Index