Von Neumann algebras are weakly closed *-algebras of bounded operators
on a Hilbert space. They naturally arise in the context of
representation theory, ergodic theory and measurable group theory. Von
Neumann algebras come in two very different flavors, distinguished by
the key notion of amenability. After a basic introduction to von Neumann
algebras, I will give an overview of Alain Connes' classification of
amenable factors and then present the groundbreaking work of Amine
Marrakchi on the structure of nonamenable factors of type III.