This advanced comprehensive textbook introduces the practical application of phase diagrams to the thermodynamics of materials consisting of several phases. It describes the fundamental physics and thermodynamics as well as experimental methods, treating all material classes: metals, glasses, ceramics, polymers, organic materials, aqueous solutions. With many application examples and realistic cases from chemistry and materials science, it is intended for students and researchers in chemistry, metallurgy, mineralogy, and materials science as well as in engineering and physics. The authors treat the nucleation of phase transitions, the production and stability of technologically important metastable phases, and metallic glasses. Also concisely presented are the thermodynamics and composition of polymer systems. This innovative text puts this powerful analytical appoarch into a readily understandable and practical context, perhaps for the first time.