INTRODUCTION vii I. THE CLASSICAL LINEAR GROUPS 1 II. TOPOLOGICAL GROUPS 25 III. MANIFOLDS 68 IV. ANALYTIC GROUPS. LIE GROUPS 99 V. THE DIFFERENTIAL CALCULUS 0F CARTAN 139 VI. COMPACT LIE GROUPS AND THEIR REPRESENTATIONS 171 INDEX 215
Claude Chevalley (1909-1984) served on the faculty of Princeton University and was resident at the Institute for Advanced Study. He was a member of the Bourbaki and was awarded the Cole Prize of the American Mathematical Society.
"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