This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.

Preface to the Second Edition * Preface to the First Edition * List of Figures * Prerequisites by Chapter * Standard Notation * Introduction: Closed Linear Groups * Lie Algebras and Lie Groups * Complex Semisimple Lie Algebras * Universal Enveloping Algebra * Compact Lie Groups * Finite-Dimensional Representations * Structure Theory of Semisimple Groups * Advanced Structure Theory * Integration * Induced Representations and Branching Theorems * Prehomogeneous Vector Spaces * Appendices * Hints for Solutions of Problems * Historical Notes * References * Index of Notation * Index