Rate Independent Systems : Theory and Application 1. A general view on rate independent systems 2. Energetic rate independent systems 3. Rate independent systems in Banach spaces 4. Applications in continuum mechanics and physics of solids 5. Beyond rate independence Appendices References Index This monograph provides both an introduction to and a thorough exposition of the theory of rate independent systems which the authors have worked on with a number of collaborators over many years. The focus is mostly on fully rate independent systems first on an abstract level with or without a linear structure discussing various concepts of solutions with full mathematical rigor. The usefulness of the abstract concepts is then demonstrated on the level of various applications primarily in continuum mechanics of solids including suitable approximation strategies with guaranteed numerical stability and convergence. Particular applications concern inelastic processes such as plasticity damage phase transformations or adhesive type contacts both at small strains and at finite strains. Other physical systems such as magnetic or ferroelectric materials and couplings to rate dependent thermodynamic models are also considered. Selected applications are accompanied by numerical simulations illustrating both the models and the efficiency of computational algorithms. This book presents the mathematical framework for a rigorous mathematical treatment of rate independent systems in a comprehensive form for the first time. Researchers and graduate students in applied mathematics engineering and computational physics will find this timely and well written book useful