This book focuses on careful analysis to various mathematical problems derived from shock reflection by using partial differential equations. The occurence， propagation and reflection of shock waves are important phenomena in fluid dynamics. Comparing the plenty of studies of physical experiments and numerical simulations on this subject， this book makes main efforts to develop the related theory of mathematical analysis， which is rather incomplete so far.The book first introduces some basic knowledge on the system of compressible flow and shock waves， as well as the concept of shock polar and its properties， which are first sys tematically presented and proved. Mathematical analysis of regular reflection and Mach reflection in both steady and unsteady flow arc the most essential parts of this book. To give challenges in future research， some long-standing open problems are listed in the end of this book.The book is attractive to researchers in the fields of partial differential equations， system of conservation laws， fluid dynamics and shock theory.