2 MASAMICHI TAKESAKI goes back to the group measure space construction of factors of Murray and von Neumann. It turns out that the crossed products are very useful in the structure analysis of factors of type III. Indeed, every von Neumann algebra of type III will be shown to be the crossed product of a von Neumann algebra of type 11^ by a trace scaling one parameter group of automorphisms. Furthermore, the outer conjugacy analysis of the automorphism group of the AFD fac- tor of type II÷ enabled A. Connes to give intrinsic characterizations of AFD von Neumann algebras and to describe their algebraic structure in far reaching detail. We shall describe the development of the structure theory of factors during the period from 1968 through 1975, starting from the Tomita-Takesaki theory and ending with Connes' theory of injective factors. The author would like to express his thanks to the Organizer Professor Paul Muhly and his colleagues at the Department of Mathematics, University of Iowa, for arranging the Con- ference. He thanks also Joanne S. Kirk for the skillful typing of the manuscript.
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