This graduate text is indispensable for those wanting to see and understand the mechanics of extreme dynamic events. It describes in detail the mechanics and material models used in understanding impact and penetration events. Covers continuum mechanics, the Hugoniot jump conditions, plasticity theory, damage and failure theory, shock and wave propagation in both Eulerian and Lagrangian frameworks, and the high pressure and high-rate response of materials. Nonlinearity in response of materials and systems is a common theme, showing itself in interesting and surprising ways. Materials are studied through damage to failure, since in armor and protection applications materials are utilized all the way through failure. Continuum and constitutive modelling topics required for modern large-scale numerical simulation techniques are clearly described. Extensive exercises ensure comprehension and explore new topics. This text is appropriate for a variety of graduate courses, including Continuum Mechanics, Advanced Solid Mechanics, and Plasticity and Inelasticity Theory.