Lectures on Electric-Magnetic Duality and the Geometric Langlands Program

These lecture notes are based on the master class given at the Cen-ter for the Topology and Quantization of Moduli Spaces, University of Aarhus, August 2007. I provide an introduction to the recent work on the Montonen-Olive duality of N = 4 super-Yang-Mills theory and the Geometric Langlands Program.