Providing a basic foundation for advanced graduate study and research in the mechanics of solids, this treatise contains a systematic development of the fundamentals of finite inelastic deformations of heterogeneous materials. The book combines the mathematical rigor of solid mechanics with the physics-based micro-structural understanding of the materials science, to present a coherent picture of finite inelastic deformation of single and polycrystalline metals, over broad ranges of strain rates and temperatures. It also includes a similarly rigorous and experimentally-based development of the quasi-static deformation of cohesionless granular materials that support the applied loads through contact friction. Every effort has been made to provide a thorough treatment of the subject, rendering the book accessible to students in solid mechanics and the mechanics of materials. This is the only book that seamlessly integrates rigorous mathematical description of finite deformations with mechanisms based on micromechanics to produce useful results with relevance to practical problems.