This book is particularly intended for first-year graduate students in mechanical and structural engineering who are taking any of the courses of continuum mechanics, elasticity, or plasticity. Having said that, the material in this book is suitable for all science and engineering majors since it covers much more material and in greater depth than those existing in the ¿mathematical preliminaries¿ sections of a typical book of continuum mechanics and related subjects. Vectors, tensors, both in Cartesian and curvilinear coordinates, and matrix methods are fundamental and indispensable tools for understanding and dealing with a vast range of phenomena in modern nonlinear continuum mechanics. Although the primary purpose of this book is to formulate and present the mathematical structure of the theory of a vast range of deformation phenomena (finite elastic, viscoelastic, plastic, etc), by the notation and techniques involved, it is quite general and apt to be used in any branch of classical theoretical physics. The book is essentially self-contained, assuming only the standard undergraduate preparation in mechanical and related engineering curricula.