New in paperback. Hardcover was published in 2012. This book provides a complete and comprehensive overview of ultracold lattice gases as quantum simulators. It opens up an interdisciplinary field involving atomic, molecular and optical physics, quantum optics, quantum information, condensed matter and high energy physics. "This masterpiece is a unique opportunity to learn about the frontiers of quantum many-body physics, and how they can be explored with ultracold atoms in optical lattices. Some of the most talented theorists in the field guide the readers through the fascinating interplay of atomic, optical and condensed-matter physics, where old and new quantum many-body phenomena appear." - Giovanni Modugno, Universita di Firenze.