After an introduction to materials science aspects and experimental findings, the author presents the key fundamentals of continuum mechanics (kinematics, statics, dynamics). The focus is on the theory of finite deformations. Given the increasing use of modern materials that do not behave in a linear elastic and isotropic manner or where large deformations occur, tensor functions are of fundamental importance for continuum mechanics. The author extensively discusses the elastic and inelastic behavior of isotropic and anisotropic materials (solids and fluids), incorporating geometric and physical nonlinearities. The new edition represents a significant expansion of the original version, which was limited to a classification of continuum mechanics into elastodynamics, plasticity, and creep mechanics, and includes numerous additions.