Theory of Lie Groups - (Dover Books on Mathematics) by Claude Chevalley (Paperback)

This comprehensive and authoritative text on Lie Groups by Claude Chevalley is a must-read for advanced undergraduate and graduate students of mathematics.

With a focus on the global viewpoint and analytic manifolds, this book provides a systematic exposition of the foundations of Lie group theory, covering classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. The author's most important contribution to mathematics is his work on group theory, and this text remains the basic reference on Lie groups for at least two decades.

The treatment opens with an overview of the classical linear groups and of topological groups, followed by an examination of the theory of analytic manifolds and a combination of the notions of topological group and manifold that defines analytic and Lie groups. The book also includes an exposition of the differential calculus of Cartan and concludes with an exploration of compact Lie groups and their representations.

With its emphasis on the global viewpoint and analytic manifolds, this text is essential for anyone looking to gain a deep understanding of Lie group theory and its applications in mathematics and physics.