Representation theory is one of the most applied fields of mathematics. It was developed answering questions arising from physics. This book is a survey on the representation theory of skew group algebras. It has essentially three parts. In the first part the author presents the basic notions and results regarding the representation theory of finite dimensional algebras. In the second part skew group algebras are defined, and some basic properties are presented, via several examples. This part also contains recent results regarding the topic, namely new combinatorial methods developed to examine the basic algebra of the skew group algebra of a path algebra. The last part contains applications of skew group algebras in the theory of Galois coverings, first on rings and then on Abelian categories.