Based on lectures delivered to the Seminar on Operator Algebras at
Oakland University during the Winter semesters of 1985 and 1986, these
notes are a detailed exposition of recent work of A. Connes and U.
Haagerup which together constitute a proof that all injective factors of
type III1 which act on a separable Hilbert space are isomorphic. This
result disposes of the final open case in the classification of the
separably acting injective factors, and is one of the outstanding recent
achievements in the theory of operator algebras. The notes will be of
considerable interest to specialists in operator algebras, operator
theory and workers in allied areas such as quantum statistical mechanics
and the theory of group representations.