Theory of Lie Groups Dover Boo

"Chevalley's most important contribution to mathematics is certainly his work on group theory. . . . [Theory of Lie Groups] was the first systematic exposition of the foundations of Lie group theory consistently adopting the global viewpoint, based on the notion of analytic manifold. This book remained the basic reference on Lie groups for at least two decades." — Bulletin of the American Mathematical Society
Suitable for advanced undergraduate and graduate students of mathematics, this enduringly relevant text introduces the main basic principles that govern the theory of Lie groups. The treatment opens with an overview of the classical linear groups and of topological groups, focusing on the theory of covering spaces and groups, which is developed independently from the theory of paths.
Succeeding chapters contain an examination of the theory of analytic manifolds as well as a combination of the notions of topological group and manifold that defines analytic and Lie groups. An exposition of the differential calculus of Cartan follows and concludes with an exploration of compact Lie groups and their representations.

Claude Chevalley (1909–84) received his doctorate in mathematics from the University of Paris in 1933 and was later at the Institute for Advanced Study in Princeton, New Jersey, and on the faculty of Columbia University. In the 1950s he returned to France and taught at his alma mater. In addition to his work on group theory, he made major contributions to several other areas of mathematics, including number theory and algebraic geometry. He was a member of the Bourbaki group and received the Cole Prize of the American Mathematical Society in 1941. His other books include Introduction to the Theory of Algebraic Functions of One Variable.