2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69038We give a survey on L^2-invariants such as L^2-Betti numbers and L^2-torsion taking an algebraic point of view. We discuss their basic definitions, properties and applications to problems arising in topology, geometry, group theory and K-theory.95 pages, based on lectures given at the LMS Durham Proceedings on Geometry and Cohomology in Group Theory in July 2003Geometric Topology57S99;46L99;18G15;19A99;19B99;200C07;20F25text