Contents Introduction x i Lecture 1. von Neumann Algebras 1 1.1. Thre e topologies on 3§{%?) 1 1.2. vo n Neumann's bicommutant theore m 2 1.3. (Concrete ) vo n Neumann algebra s 2 1.4. Factor s 3 1.5. Example s of factors 4 1.6. Compariso n o f projections 6 1.7. Type s I, Hi, Hoc, and II I factors 7 1.8. Standar d for m fo r H i factor s 7 1.9. Th e fundamental grou p of a Hi facto r 8 1.10. Typ e III factors 9 1.11. Hyperfinitenes s 1 0 Lecture 2. Grou p Actions and Subfactors 1 3 2.1. Th e coupling constant 1 3 2.2. Galoi s theory fo r finite group actions 1 4 2.3. Connes ' results on automorphisms o f R 1 5 2.4. Extension s o f Connes' automorphism result s 1 6 vii
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