-Finite-dimensional representations:
Poincare-Birkhoff-Witt theorem, Theorem of the highest weight, Complete reducibility, Harish-Chandra isomorphism theorem, Weyl character formula, Parabolic subalgebras, Application to compact Lie groups.

-Structure theory of semisimple groups:
Compact real forms, Cartan decomposition, Iwasawa decomposition, Uniqueness properties of the Iwasawa decomposition, Caylay Transforms, Vogan diagrams, Classification of simple real Lie algebras.

-Advanced structure theory (期末報告內容)