Sofic Approximation of Groups

In this paper, we discuss sofic approximation of groups. We first discuss two equivalent definitions of a group to be sofic, in which we will introduce ultrafilter and its applications. We also discuss specific examples of sofic groups and some interesting properties of them. Section two to five form a survey of previous results. In section six, we prove a generalization of a special case of Elek-Szabo Uniqueness.