Introduction to L^2-invariants

We give a basic introduction to L^{^2}-invariants. We first discuss the necessary tools from operator theory such as  group von Neumann algebras, Murray-von Neumann dimension, spectral density functions and then
present  basic invariants such as L^{^2}-Betti numbers and L^{^2}-torsion. Finally we review some
applications to geometry, topology and group theory. This talk aims at a general audience.