This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the modeltheoretic study of groups, i.e., into what can be said about groups, and for that matter, about all the traditional algebraic objects. The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then, whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described. The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic. Readership Graduate students and research mathematicians working in logic and in algebra. Reviews From a review of the French edition: "This is a beautiful book in which almost everything known about stable groups appears."  Zentralblatt MATH Table of Contents  A couple of words about groups
 Introduction
 Chain
 Structure
 Fields
 Geometry
 Generics
 Rank
 Weight
 Bibliography
 Index
 Postscript: Thirteen years later
