Representations of the group $GL(n,F)$ where $F$ is a non-Archimedean local field

This article is a survey of recent results in the theory of representations of reductive $\wp$-adic groups. For simplicity of presentation only the groups $GL(n)$ are treated. Chapter I provides general information on representations of locally compact zero-dimensional groups. Chapter II presents Harish-Chandra's method of studying the representations of $GL(n)$, which is based on reduction to cuspidal representations. Some finiteness theorems are proved by this method. In Chapter III we study another approach to the representations of $GL(n)$, due to Gel'fand and Kazhdan; it is based on restricting the representations from $GL(n)$ to a subgroup $P_n$. All theorems are presented with detailed proofs. No prior information is assumed on the part of the reader except the most elementary familiarity with the structure of non-Archimedean local fields.