Fluid Dynamics : Lectures given at the 3rd 1982 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Varenna Italy August 22 – September 1 1982 § 1. Introduction and motivation Smooth solutions for the equations of compressible and incompressible fluid flow The linear transport operator of fluid dynamics Limites des equations d’un fluide compressible lorsque la compressibilite tend vers zero Vortex theory and euler and navier stokes evolution in two dimensions Free boundary problems for compressible viscous fluids.