Pavel Etingof, Massachusetts Institute of Technology, Cambridge, MA, USAOleg Golberg, Sebastian Hensel: Universität Bonn, Bonn, GermanyTiankai Liu, Massachusetts Institute of Technology, Cambridge, MA, USAAlex Schwendner, Two Sigma Investments, New York, NY, USADmitry Vaintrob, Harvard University, Cambridge, MA, USAElena Yudovina, University of Cambridge, Cambridge, United Kingdomwith historical interludes by Slava Gerovitch, Massachusetts Institute of Technology, Cambridge, MA, USA

• IntroductionBasic notions of representation theoryGeneral results of representation theoryRepresentations of finite groups: Basic resultsRepresentations of finite groups: Further resultsQuiver representationsIntroduction to categoriesHomological algebraStructure of finite dimensional algebrasReferences for historical interludesBibliographyIndex

This charming book ... the material in the book is quite modern, the unifying theme being the representation theory of associative algebras, and the presentation is very accessible. ...It is a truly wonderful achievement. The book is well-written, sportingly paced, and brims with mathematical elegance: the prose is clear and tight and the proofs are compact and pretty." - MAA Reviews"The book gives a concise introduction to various aspects of representation theory. It is an interesting addition to the existing literature on the subject." - Mathematical Reviews"Add to this the sets of problems included in the book, replete with occasional hints and estimates of the degree of difficulty, as well as the wonderful 'Historical Interludes' by Slava Gerovitch, and the result is a fantastic little book. I think it is bound to become the way to get into this subject 'holistically.'" - MAA Reviews