Radiationless transitions comprise an important class of physical phenomena occurring in the excited states of molecules. They affect the lifetimes of the ex cited states and govern primary photochemical and photophysical processes. Much effort has been devoted to the understanding of radiationless transi tions. Still, owing to recent advances, the field continues to attract attention. The demand for a book on the theory of these processes naturally arises in at tempting to comprehend a large body of literature, as the famous review article by K. F. Freed and the book by R. Englman do not encompass some issues of current interest. Our intent is to highlight the underlying physical principles and methods in such a way that the book both in its content and its presentation is instruc tive for a wide audience. The basic ideas are treated in simple mathematical terms intelligible to ex perimentalists and to readers unfamiliar with the field. Complicated theoret ical methods are always expounded from first principles, so that a knowledge of quantum mechanics and mathematics at the graduate-student level will enable the reader to easily follow the derivations. Experts will find efficient methods of calculating the transition rates, as well as new applications of quasiclassical methods and fresh treatments of standard problems. Details of measurements are not discussed, and experimental data are only invoked to illustrate the theory."