This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form.The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings with several objects, the...