Memoirs of the American Mathematical Society 2004; 227 pp; softcover Volume: 169 ISBN10: 0821834827 ISBN13: 9780821834824 List Price: US$79 Individual Members: US$47.40 Institutional Members: US$63.20 Order Code: MEMO/169/802
 In this paper we complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small. A number of consequences are obtained. It follows from the main theorem that a simple algebraic group over an algebraically closed field has only finitely many conjugacy classes of maximal subgroups of positive dimension. It also follows that the maximal subgroups of sufficiently large order in finite exceptional groups of Lie type are known. Readership Graduate students and research mathematicians interested in group theory and generalizations. Table of Contents  Introduction
 Preliminaries
 Maximal subgroups of type \(A_1\)
 Maximal subgroups of type \(A_2\)
 Maximal subgroups of type \(B_2\)
 Maximal subgroups of type \(G_2\)
 Maximal subgroups \(X\) with rank\((X)\geq3\)
 Proofs of Corollaries 2 and 3
 Restrictions of small \(G\)modules to maximal subgroups
 The tables for Theorem 1 and Corollary 2
 Appendix: \(E_8\) structure constants
 References
