This volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or on lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book’s utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped.

The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.

Contents:

• Lie Groups and Lie Algebras: Introduction
• Lie Groups
• Haar Measure and its Applications
• Elements of the Theory of Lie Algebras
• The Structure of Compact Connected Lie Groups
• Representations of Compact Lie Groups
• Symmetric Spaces of Non-compact Type
• Semisimple Lie Algebras and Lie Groups
• Lattices in Lie Groups
• Density Results for Cofinite Volume Subgroups