Pham Huu Tiep
:Semisimple Lie algebras are some of the fundamental concepts of Algebra, which have proved to be useful in many areas of mathematics and physics. This course will be an introduction to the theory of semisimple Lie algebras, with emphasis on representations.
Topics will include elementary properties of Lie algebras, theorems of Lie and Cartan, conjugacy of Borel subalgebras, root systems and their construction, structure and classification of semisimple Lie algebras, and representation theory of semsimple.
Lie algebras (if time permits).
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer Verlag, 3rd printing, 1980
Good knowledge of linear algebra and some acquaintance with abstract algebra (say first semester of Abstract Algebra for graduate students).