This book, authored by M. A. Biot, is a valuable and interesting contribution to the field of nonlinear elasticity and viscoelasticity. It builds upon the author's earlier work and recent papers on stability and thermodynamics. The book presents a rigorous but intermediate theory that bridges the gap between formal mathematical approaches and practical engineering treatments. It extends the methods of "strength of materials" to three dimensions and avoids the use of tensor calculus, instead relying on suffix notation and Cartesian tensors. The concepts are developed in the context of linearized mechanics under initial stress, offering new insights into areas such as rubber elasticity, internal gravity waves, and tectonic folding in geodynamics. The book introduces a dual representation of stress and strain, allowing for clear separation of deformation geometry and material behavior, and emphasizes variational methods and the principle of virtual work.This book, authored by M. A. Biot, is a valuable and interesting contribution to the field of nonlinear elasticity and viscoelasticity. It builds upon the author's earlier work and recent papers on stability and thermodynamics. The book presents a rigorous but intermediate theory that bridges the gap between formal mathematical approaches and practical engineering treatments. It extends the methods of "strength of materials" to three dimensions and avoids the use of tensor calculus, instead relying on suffix notation and Cartesian tensors. The concepts are developed in the context of linearized mechanics under initial stress, offering new insights into areas such as rubber elasticity, internal gravity waves, and tectonic folding in geodynamics. The book introduces a dual representation of stress and strain, allowing for clear separation of deformation geometry and material behavior, and emphasizes variational methods and the principle of virtual work.