Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects

Two dimensional Yang-Mills theory has proved to be a surprisingly rich model, despite, or possibly because of, its simplicity and tractability both in classical and quantum forms. The purpose of this article is to give a largely self-contained introduction to classical and quantum Yang-Mills theory on the plane and on compact surfaces, along with its relationship to ChernSimons theory, illustrating some of the directions of current and recent research activity.