Vladimir Retakh
This course is an introduction to the theory of Lie algebras. Lie algebras are some of the fundamental concepts of algebra, which have proved to be useful in many areas of mathematics and physics. 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 semisimple Lie algebras (if time permits).
Introduction to Lie Algebras and Representation Theory, by J. E. Humphreys, Springer-Verlag, 3rd printing, 1980
Linear algebra (on the level of Math 350) and some acquaintance with abstract algebra (on the level of Math 551).