The Bethe/Gauge Correspondence

It is well known that in order to understand QCD we have to go beyond perturbation theory. Gauge theories with supersymmetry provide a class of toy models for QCD in which we can do exact calculations.\nAnother area of theoretical physics where exact methods are used is the theory of quantum integrability, encompassing e.g. the Heisenberg model for magnetism.\nIn recent years, Nekrasov and Shatashvili have discovered a deep connection between quantum integrable models and the vacuum structure of supersymmetric gauge theories in two dimensions. In this thesis we give a self-contained introduction to these two subjects and explain the main observation underlying the Bethe/gauge correspondence.