The goal of this tutorial is to give an introduction to von Neumann algebras. After recalling the basic definitions, I will present the construction of von Neumann algebras arising from countable groups and their measure preserving actions. I will then explain how analytic properties of groups (amenability, property (T)) are used to obtain classification and rigidity results for von Neumann algebras. Finally, I will discuss the ultraproduct construction for von Neumann algebras and related open problems.
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