The theory of finite-dimensional algebras is one of the mostfundamental domains of modern algebra, applied in severalother parts of mathematics andin theoretical physics. Thisbook, written by two of the leading researchersin the fieldand revised and augmented for the English edition, wastranslated from the Russian by a third leading specialist,who has contributed to it an appendix.The book presents both the basic classical theory and morerecent results closely related to current research (somecategory theory including Morita's theorem, schemes ofquivers andtensor algebras, duality, quasi-Frobenius,hereditary, serial algebras). Theonly prior knowledgeassumed of the reader is linear algebra and, in places,alittle group theory. Each chapter includes a series ofexercises, illustrating the content and introducing morerefined results: for the more complicated ones, hints forthe solution are given - thus the book can be used as atextbook in class or for self-study, and as an up-to-datereference to the field.