The goal of this text is to present some of the basic ideas of fluid mechanics in a mathematically attractive manner, to present the physical background and motivation for some constructions that have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems and to interest some of the students in this beautiful and difficult subject. The third edition has incorporated a number of updates and revisions, but the spirit and scope of the original book are unaltered.