This monograph provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. For scalar hyperbolic conservation laws, the well posedness of the initial problem in the whole space as well as the initial boundary value problem in bounded domains is treated. Further, one of the first rigorous mathematical treatments of a class of non-Newtonian fluids is given. The new results, obtained here for both problems, have applications to many rapidly developing areas of physics, biology and mechanical engineering. Weak and Measure-valued Solutions to Evolutionary PDEs will be of interest to researchers and graduate students in mathematics, theoretical physics and engineering. In particular, engineers and physicists involved in fluid mechanics research, and mathematicians interested in PDEs will value this monograph.