Includes bibliographical references.

PART I. LONG LECTURES: Quantum impurity problems in condensed matter physics / Ian Affleck -- Conformal field theory and statistical mechanics / John Cardy -- The quantum Hall effect / F. Duncan and M. Haldane -- Topological phases and quantum computation / Alexei Kitaev -- Four lectures on computational statistical physics / Werner Krauth -- Loop models / Bernard Nienhuis -- Lectures on the integrability of the six-vertex model / Nicolai Reshetikhin -- Mathematical aspects of 2D phase transitions / Wendelin Werner -- PART II. SHORT LECTURES: Numerical simulations of quantum statistical mechanics models / Fabien Alet -- Rapidly rotating atomic Bose gases / Nigel R. Cooper -- The quantum Hall effect / Jurg Frohlich -- The dimer model / Richard Kenyon -- Boundary loop models and 2D quantum gravity / Ivan Kostov -- Real-space condensation in stochastic mass transport models / Satya N. Majumdar -- Quantum spin liquids / Grégoire Misguich -- Superspin chains and supersigma models: a short introduction / Hubert Saleur -- Integrability and combinatorics: selected topics / Paul Zinn-Justin -- PART III. SEMINARS: A rigorous perspective on Liouville quantum gravity and the KPZ relation / Bertrand Duplantier -- Topologically protected qubits based on Josepshon junction arrays / Mikhail V. Feigel'man -- On some quantum Hall states with negative flux / Thierry Jolicoeur -- Supersolidity and what soluble models can tell us about it / David Thouless.

"Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics."--Publisher's description.