Book excerpt: The present theoretical and experimental knowledge of the time evolution of a system during solidification, not only in equilibrium, but also in nonequilibrium conditions, is summarized in this book. Such knowledge is of fundamental importance for the determination of the constitution of materials or of the technological conditions necessary to prepare materials with a desired structure. Emphasizing the importance of kinetic phase diagrams, the authors focus the attention of the reader on the problems connected with nonequilibrium conditions, that are encountered during real phase transformations. A critical review of phenomenological and statistical theories of phase transformations and of mass and heat transport enables the reader to determine the range of applicability of concrete models for the description of the evolution of a given system. The book is supplemented with several less-known methods and results of phase characterization, including a detailed account of the Soviet school of T.A. Cherepanova which is not well known in the West. The text also covers the modern research area of glasses and their preparation.