Aimed at researchers and graduate students in mathematics, mechanical engineering, material science and physics. The second edition of this classic text has been completely revised. The original edition was designed to introduce the serious, mathematically inclined student to modern mechanics of continua and the book still serves that purpose well. In the new edition, more emphasis is put on applications. There are new sections concerning universal solutions for incompressible materials and fluids presented in the spatial description. The concept of "universe of shapes" is introduced as a means of dealing with bodies in the actual shapes they occupy as time goes on. The text includes many special problems and solutions not found in other books. Attention is called to yet unsolved problems.