  These lecture notes give an overview of recent results in geometric Langlands
correspondence which may yield applications to quantum field theory. We start
with a motivated introduction to the Langlands Program, including its geometric
reformulation, addressed primarily to physicists. I tried to make it as
self-contained as possible, requiring very little mathematical background.
Next, we describe the connections between the Langlands Program and
two-dimensional conformal field theory that have been found in the last few
years. These connections give us important insights into the physical
implications of the Langlands duality.
