We shall introduce the affine Grassmanian Gr of a reductive connected algebraic group G over C, the category of spherical perverse sheaves on Gr, a convolution product on these sheaves, and use the Tannakian formalism to show that this category is equivalent to that of finite dimensional complex representations of the dual group of G. This is a first step in Drinfeld's ``geometric Langlands program". In fact these lectures would attempt to understand the terms mentioned here, outline some proofs and constructions, and perhaps get to some applications.

Some basic algebra, such as algebraic groups, sheaves.

I. Mirkovic, K. Vilonen. Geometric Langlands duality and representations of algebraic groups over commutative rings. Annals of Math. 166 (2007), 95-143.