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.

Review

This is a text on the elementary theory of Lie groups and Lie algebras, suitable for graduate or advanced undergraduate students in mathematics ... The book presents some interesting topics often omitted from first courses in Lie theory ... --Mathematical Reviews

It is as self-contained as possible and introduces the rich world of Lie groups and Lie algebras. Many exercises give the opportunity to learn the subject more deeply. --Zentralblatt MATH

I recommend this book for everybody starting to apply, learn or teach Lie theory, and also for researchers whose work is related to Lie theory. Anybody who has anything to do with Lie theory should place this book on his/her bookshelf. --Acta Scientiarum Mathematicarum

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