Translated from the second Russian edition and with added notes by K.A. Hirsch. Teoriya Grupp by Kurosh was widely acclaimed, in its first edition, as the first modern text on the general theory of groups, with the major emphasis on infinite groups. The decade that followed brought about a remarkable growth and maturity in the theory of groups, so that this second edition, an English translation, represents a complete rewriting of the first edition. The book can be used as a beginning text, the only requirement being some mathematical maturity and a knowledge of the elements of transfinite numbers. Many new sections were added to this second edition, and many old ones were completely revised: The theory of abelian groups was significantly revised; many significant additions were made to the section on the theory of free groups and free products; an entire chapter is devoted to group extensions; and the deep changes in the theory of solvable and nilpotent groups — one of the large and rich branches of the theory of groups — are covered in this work. Each volume concludes with Editor's Notes and a Bibliography.