Since Chevalley showed in 1955 how to construct analogues of the complex simple Lie groups over arbitrary fields, these 'simple groups of Lie type' and their twisted analogues have been the subject of detailed investigation from a number of different points of view. This book is intended to serve as an introduction to the theory of Chevalley groups. It is not an exhaustive account of these groups, but concentrates on the basic results in the structure theory of the Chevalley groups and the twisted groups.
The Chevalley groups are studied in this book as groups of automorphisms of Lie algebras. This approach implies a concentration on the adjoint Chevalley groups—indeed the universal Chevalley groups and other isogenous groups have only been touched on in the development. In developing the theory we have found it necessary to assume a certain familiarity with the theory of simple Lie algebras over the complex field. Fortunately several good accounts of this theory are now available, and the information which we need about the simple Lie algebras has been collected together in a survey chapter...