Since the fifties, the theory of partial differential equations has undergone considerable development, yet it is certainly one of those fields where we find both the largest number of research articles and the smallest number of works of synthesis. The specialist can come to terms with such a situation, but the student who desires an introduction to this theory finds it rather a handicap. Thus, in the present book, which is not a treatise but an introduction, we aim to present a reasonably large range of recent methods: pseudo-differential operators, oscillatory integrals, stationary phase expansion, microlocalis-ation... We show how these methods permit the solution of numerous classical problems in an elegant and general manner: elliptic equations, boundary problems, evolution equations, mixed hyperbolic problems... We have allotted considerable room to the equations of Physics because, historically, this has been the origin of important problems in partial differential equations and remains to the present day the principal source of interesting questions.