The content of this book corresponds to a one-semester course taught at the University of Paris-Sud (Orsay) in the spring 1994. It is accessible to students or researchers with a basic elementary knowledge of Partial Dif­ ferential Equations, especially of hyperbolic PDE (Cauchy problem, wave operator, energy inequality, finite speed of propagation, symmetric systems, etc.). This course is not some final encyclopedic reference gathering all avail­ able results. We tried instead to provide a short synthetic view of what we believe are the main results obtained so far, with self-contained proofs. In fact, many of the most important questions in the field are still completely open,