0 Introduction. - 0. 1 Basic operator theory. - 0. 2 The predual L(H)*. - 0. 3 Three locally convex topologies on L(H). - 0. 4 The double commutant theorem. - 1 The Murray von Neumann Classification of Factors. - 1. 1 The relation ~ (rel M). - 1. 2 Finite projections. - 1. 3 The dimension function. - 2 The Tomita Takesaki Theory. - 2. 1 Noncommutative integration. - 2. 2 The GNS construction. - 2. 3 The Tomita-Takesaki theorem (for states). - 2. 4 Weights and generalized Hilbert algebras. - 2. 5 The KMS boundary condition. - 2. 6 The Radon-Nikodym theorem and conditional expectations. - 3 The Connes Classification of Type III Factors. - 3. 1 The unitary cocycle theorem. - 3. 2 The Arveson spectrum of an action. - 3. 3 The Connes spectrum of an action. - 3. 4 Alternative descriptions of ?(M). - 4 Crossed-Products. - 4. 1 Discrete crossed-products. - 4. 2 The modular operator for a discrete crossed-product. - 4. 3 Examples of factors. - 4. 4 Continuous crossed-products and Takesaki's duality theorem. - 4. 5 The structure of properly infinite von Neumann algebras. - Appendix: Topological Groups. - Notes. Language: English