This volume presents for the first time in book form the mathematical principles underlying the Large Eddy Simulation (LES) method, which is rapidly finding new practical applications in engineering. LES seeks to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. Since its introduction in 1970, LES has matured into a highly-developed computational technology, using the tools of turbulence theory and the experience gained from practical computation. This book teaches the mathematical foundations of LES and its models and connects the powerful tools of applied mathematics, partial differential equations and LES.