Preface. Introduction. Simple locally finite groups; B. Hartley. Algebraic groups; G.M. Seitz. Subgroups of simple algebraic groups and related finite and locally finite groups of Lie type; M.W. Liebeck. Finite simple groups and permutation groups; J. Saxl. Finitary linear groups: a survey; R.E. Phillips. Locally finite simple groups of finitary linear transformations; J.I. Hall. Non-finitary locally finite simple groups; U. Meierfrankenfeld. Inert subgroups in simple locally finite groups; V.V. Belyaev. Group rings of simple locally finite groups; A.E. Zalesskii. Simple locally finite groups of finite Morley rank and odd type; A.V. Borovik. Existentially closed groups in specific classes; F. Leinen. Groups acting on polynomial algebras; R.M. Bryant. Characters and sets of primes for solvable groups; I.M. Isaacs. Character theory and length problems; A. Turull. Finite p-groups; A. Shalev. Index.