An introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. Covering the essentials of the subject, starting from basic undergraduate mathematics, it proceeds through the fundamentals of Lie theory up to topics in representation theory, such as the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

• Preface


• 1: The exponential map


• 2: Lie theory


• 3: The classical groups


• 4: Manifolds, homogeneous spaces, Lie groups


• 5: Integration


• 6: Representations


• Appendix: Analytic Functions and Inverse Function Theorem


• References


• Index