  These are lecture notes (by the first author) from a course (by the second
author) given over two extended semesters at the University of Sydney. The
first part provides an introduction to the Langlands correspondence from an
arithmetical point of view. The second part gives enough background in
geometric representation theory to understand Bezrukavnikov's equivalence,
which is a categorification of Kazhdan and Lusztig's two realizations of the
affine Hecke algebra.
