Introduction

Abstract

Of all topological algebraic structures compact topological groups have perhaps the richest theory since so many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geometry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again play a role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory.