The Yang-Mills Moduli Space and The Nahm Transform

Abstract

In this thesis we will discuss gauge theories and instantons. We will start with discussing the necessary analysis to define the Yang-Mills moduli space. This includes Sobolev spaces, Fredholm transversality and elliptic differential operators. The Nahm transform over the four-torus is defined and proved to be an involution. Finally we will discuss the ADHM construction.