This volume contains survey papers on the theory of operator algebras based on lectures given at the ""Lluís Santaló"" Summer School of the Real Sociedad Matemática Española, held in July 2008 at the Universidad Internacional Menéndez Pelayo, in Santander (Spain).

Topics in this volume cover current fundamental aspects of the theory of operator algebras, which have important applications such as:



$K$-Theory, the Cuntz semigroup, and Classification for $C^*$-algebras
Modular Theory for von Neumann algebras and applications to Quantum Field Theory
Amenability, Hyperbolic Groups, and Operator Algebras.

The theory of operator algebras, introduced in the thirties by J. von Neumann and F. J. Murray, was developed in close relationship with fundamental aspects of functional analysis, ergodic theory, harmonic analysis, and quantum physics. More recently, this field has shown many other fruitful interrelations with several areas of mathematics and mathematical physics.

This book is published in cooperation with Real Sociedad Matemática Española (RSME).