I. Contents：
In the first semester, the course would cover basic Lie group theory and representation theory of compact Lie groups.
-Basic Lie Group Theory.
-Elementary Representation Theory.
-Maximal Tori and Root System.
-Weyl Integration formula; Weyl Character formula.
II. Course prerequisite：
Linear Algebra. Some knowledge on Algebra, Differential Manifolds.

III. Reference material ( textbook(s) )：
No definite textbook for this course. Students should consult
Adams, J. F., Lectures on Lie Groups, 1969, W.A.Benjamin
Cter, R., Segal, G., Macdonald, Ian, Lectures on Lie Groups and Lie Algebras,LMS student text 32, 1995, Cambridge(first two lecture series),
Brocker, T., Dieck, T.t., Representaions of Compact Lie Groups, GTM98, 1985, Springer
For those who is not familiar with differential manifold, one could consult
Warner, F., Foundatons of Differential Manifolds and Lie Groups, 1971, Scott, Foresman and Co.

IV. Grading scheme：
40% mid term + 40% final +20% report.

V. Others：