This book is an extended version of a course on continuum mechanics taught by the authors to junior graduate students in mathematics. Besides a thorough description of the fundamental parts of continuum mechanics, it contains ramifications in a number of adjacent subjects such as magnetohydrodynamics, combustion, geophysical fluid dynamics, and linear and nonlinear waves. As is, the book should appeal to a broad audience: mathematicians (students and researchers) interested in an introduction to these subjects, engineers, and scientists.

This book can be described as an “interfacial” book: interfaces between mathematics and a number of important areas of sciences. It can also be described by what it is not: it is not a book of mathematics: the mathematical language is simple, only the basic tools of calculus and linear algebra are needed. This book is not a treatise of continuum mechanics: although it contains a thorough but concise description of many subjects, it leaves aside many developments which are fundamental but not needed in practical applications and utilizations of mechanics, e.g., the intrinsic – frame invariance – character of certain quantities or the coherence of certain definitions. The reader interested by these issues is referred to the many excellent mechanics books which are available, such as those quoted in the list of references to Part I. Finally, by its size limitations, this book cannot be encyclopedic, and many choices have been made for the content; a number of subjects introduced in this book can be developed themselves into a full book.