Quantum phase transitions Describing the physical properties of quantum materials near critical points with long range many body quantum entanglement this book introduces readers to the basic theory of quantum phases their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances such as the Fermi gas near unitarity Dirac fermions Fermi liquids and their phase transitions quantum magnetism and solvable models obtained from string theory. After introducing the basic theory it moves on to a detailed description of the canonical quantum critical phase diagram at non zero temperatures. Finally a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory