This book collects lecture courses and seminars given at the Les Houches Summer School 2010 on "Quantum Theory: From Small to Large Scales". Fundamental quantum phenomena appear on all scales, from microscopic to macroscopic. Some of the pertinent questions include the onset of decoherence, the dynamics of collective modes, the influence of external randomness and the emergence of dissipative behaviour. Our understanding of such phenomena has been advanced by the study of model systems and by the derivation and analysis of effective dynamics for large systems and over long times. In this field, research in mathematical physics has regularly contributed results that were recognized as essential in the physics community. During the last few years, the key questions have been sharpened and progress on answering them has been particularly strong. This book reviews the state-of-the-art developments in this field and provides the necessary background for future studies. All chapters
are written from a pedagogical perspective, making the book accessible to master and PhD students and researchers willing to enter this field.

About the Author:
Jurg Frohlich is Professor at ETH Zurich, Switzerland. In 1984, he was awarded the "Latsis Prize" of the Swiss National Science Foundation. He has also been awarded the Marcel-Benoist Prize 1997, and, in 2001, the Max-
Planck Medal of the German Physical Society. He is a member of the "Academia Europaea" and has been elected an associate member of the "Berlin-Brandenburgische Akademie der Wissenschaften".

Manfred Salmhofer is Professor at Universitat Heidelberg, Germany. His main research interests are theoretical and mathematical physics, in particular quantum field theory and statistical mechanics, the renormalization group, and condensed-matter theory. He presently acts as an associate editor of Journal of Mathematical Physics and as an Editor of Communications in Mathematical Physics.

Vieri Mastropietro is Professor at Universita' di Roma Tor Vergata. His main scientific interests are classical and
quantum Statistical Physics and Quantum Field Theory systems, analyzed through rigorous Renormalization Group methods; he has also worked on dynamical systems and KAM theory. He was awarded the Persico prize (1987 and 1989) of the Accademia dei Lincei and the Annales Poincare' prize (2006). He also acts as an editor of Annales Poincare' and CPAA and is member of the Center for Mathematical and Theoretical Physics (CMTP).

Wojciech De Roeck is a lecturer at Universitat Heidelberg, Germany. He obtained his Physics Degree at the University of Antwerp (UA) in 2002 and his PhD at the University of Antwerp and K.U.Leuven in 2006. From 2007 to 2009, he was a post-doctoral fellow supported by the FWO (Flemish Research Fund).

Leticia F. Cugliandolo is Professor at Universite Pierre et Marie Curie, France. She got her PhD in Physics from Universidad Nacional de La Plata, Argentina, in 1991. Subsequently, she spent a three year post-doc at Universita di Roma I, La Sapienza, and then moved to the Service de Physique de l'Etat Condense at Saclay
(CEA) and Ecole Normale Superieure (ENS) de Paris for a second post-doctoral experience. In 1997 she became assistant professor at ENS Paris and in 2003 full professor at Universite Pierre et Marie Curie - Paris VI where she presently teaches and pursues her research acivities. Since January 2007 she is the Director of Ecole de Physique des Houches.