This book collects together the lecture courses and seminars given at the Les Houches Summer School 2008 on Long-Range Interacting Systems, reviewing the state-of-the-art developments in this field and providing an essential background to future studies, all in writing that is accessible to Masters and PhD students and researchers wishing to enter this field. Leading scientists in different fields of mathematics and physics present their views on this fast growing and interdisciplinary field of research, exploring such topics as fundamental problems of probability, transport theory, equilibrium and non-equilibrium statistical mechanics, condensed matter physics, astrophysics and cosmology, physics of plasmas, and hydrodynamics. In particular, the book examines the thermodynamic and dynamical properties of systems with long-range interactions, which have been poorly understood until recently.