The goal of the course is to give a detailed introduction to representations of the most important infinite-dimensional Lie algebras -- namely, Heisenberg algebras, current algebras, affine Kac-Moody algebras, Lie algebras of vector fields, Virasoro algebra. I plan to cover the main statements about highest weight representations of these algebras and some related computations of Lie algebra cohomology. I will also discuss some applications of this theory to Combinatorics and Geometry. 

I will mainly follow the notes of the same named course by Pavel Etingof. The textbooks for the course are V.Kac and A.Raina ``Highest weight representations of infinite dimensional Lie algebras'' and V.Kac ``Infinite dimensional Lie algebras''. For the topics related to cohomology of Lie algebras, the book ``Cohomology of infinite-dimensional Lie algebras'' by D.B.Fuks will be useful. 

To officially pass the course, it will be required to solve homework assignments which will be assigned every Wednesday and due the next Wednesday.