This is the first book to logically present the major problems of the vitreous state within the framework of irreversible thermodynamics. Filled with elementary explanations for difficult problems, this easily understood text/reference treats in detail the criteria of glass transition, the peculiarities of relaxing structural parameters, and the Prigogine-Defay ratio. Based on the author's rigorous generalization of the Second Law for non-equilibrium, the book systematizes all known thermodynamic data for glasses and melts. The thermodynamic essence of structural relaxation and memory effects are considered. The viscous flow theories are treated as a constituent of the kinetic description. All theoretical questions are illustrated by comparison of calculations with the experiments for glasses of inorganic and organic nature, with special attention to structural classification. An informative review of modern structural investigations is included. The bibliography follows the history of the main problems from the nineteenth century.