The present book is devoted to problems of a physically important state of condensed matter - the vitreous state. We tried to summarize here the experimental evidence and the different theoretical approaches - structural, thermodynamic and those of statistical physics - connected with the formation, the kinetic stability and with the general nature of glasses as a particular physical state. In addition, a summary is given on the information available concerning proces ses of nucleation and crystallization of glass-forming systems, on methods of preventing or, in contrast, catalyzing crystallization in vitrifying liquids, on the kinetics of nucleation, the modes of crystal growth in undercooled melts and the devitrification of glasses. It was our aim to summarize in the present volume the basic principles and the most significant developments of a newly emerging science - glass science - and to show that, at least, in principle, any substance can exist in the vitreous state. Moreover, we have tried to demonstrate that the characteristic properties of the vitreous state may be attributed under certain conditions not only to systems with an amorphous structure (like the common glasses) but also to a number of other states of condensed matter including the crystalline one.