I.Contents：
Classical Invariant Theory, Schur- Weyl Duality, Lie algebra cohomology, Harish- Chandra , isomorphism, Casselman- Osborne Theorem, Kostant’s u- cohomology formula.
II.Course prerequisite：
III.Reference material ( textbook(s) )：
A. Knapp: Lie Groups, Lie Algebras and cohomologyR. Goodman, N. Wallach: Representations and Invariants of the classical groups
IV.Grading scheme：
Presentations in class