Shock waves This book presents the fundamentals of the shock wave theory. Shock waves are present in many natural situations as a consequence of nonlinear constitutive relations. Mathematical analysis of shock waves is based mostly on the conservation laws. Consider the case of gas dynamics. There is the conservation of mass. The conservation of momentum follows from the Newtonian physics. During the nineteenth century the conservation of energy and the second law of thermodynamics were formulated. This is the scientific background when Stokes [119] and Riemann [112] did their pioneering works on shock waves in the mid nineteenth century. More conservation laws were subsequently formulated with the study of electro magnetism nonlinear elasticity high temperature gas dynamics and other physical phenomena. There have been important continuing progresses on the development of shock wave theory since the time of Stokes and Riemann.