Lecture 1: Manifolds

Lecture 2: Lie Groups I

Lecture 3: Lie Groups II

Lecture 4: Homogeneous Spaces and Lie Group Actions

*Problem set 1 due*

Lecture 5: Tensor Fields

Lecture 6: Classical Lie Groups

*Problem set 2 due*

Lecture 7: The Exponential Map of a Lie Group

Lecture 8: Lie Algebras

*Problem set 3 due*

Lecture 9: Fundamental Theorems of Lie Theory

Lecture 10: Proofs of the Fundamental Theorems of Lie Theory

*Problem set 4 due*

Lecture 11: Representations of Lie Groups and Lie Algebras

Lecture 12: The Universal Enveloping Algebra of a Lie Algebra

*Problem set 5 due*

Lecture 13: The Poincare-Birkhoff-Witt Theorem

Lecture 14: Free Lie Algebras and the Baker-Campbell-Hausdor Formula

*Problem set 6 due*

Lecture 15: Solvable and Nilpotent Lie Algebras and Theorems of Lie and Engel

Lecture 16: Semisimple and Reductive Lie Algebras, the Cartan Criteria

*Problem set 7 due*

Lecture 17: Proofs of the Cartan Criteria and Properties of Semisimple Lie Algebras

Lecture 18: Extensions of Representations, Whitehead’s Theorem, and Compete Reducibility

*Problem set 8 due*

Lecture 19: Structure of Semisimple Lie Algebras I

Lecture 20: Structure of Semisimple Lie Algebras II

*Problem set 9 due*

Lecture 21: Root Systems

Lecture 22: Properties of the Weyl Group

*Problem set 10 due*

Lecture 23: Dynkin Diagrams

Lecture 24: Construction of a Semisimple Lie Algebra from a Dynkin Diagram

*Problem set 11 due*

Lecture 25: Representation Theory of Semisimple Lie Algebras

Lecture 26: The Weyl Character Formula

*Problem set 12 due*