The purpose of this book is to present Mathematical Theory of Elasticity and its applications to a wide range of readers, including graduate students and researchers in modern theory of continuum mechanics. The book provides classical results on elasticity as well as the new findings of classical type obtained in recent years by various researchers, including the authors and the collaborators. Accessible both to those who are new to the field as well as those who have already gained as insight into the subject, the volume serves a bridge between Mathematical Theory of Elasticity through specific applications given in exercise and problems, as well as through an extensive coverage of the areas of Elastostatics, Thermoelastostatics, Elastodynamics, and Thermoelastodynamics.