The purpose of these Lecture Series notes is to offer a full overview of the present development and the potential of the Large Eddy Simulation (LES) of turbulent flows. The first part of the course notes introduces and discusses fundamental principles, presents state-of-the-art applications and possible developments of LES and Detached Eddy Simulation (DES) which represents the most promising technique to extend the usefulness of LES for high Reynolds-number flows. The second part presents applications of these approaches to various engineering fields of wide interest. The course notes are written by internationally recognized experts. Its content is addressed both to researchers interested in the fundamental simulation of turbulence and engineers wanting to apply the LES technique or LES solvers to the accurate simulations of turbulent.