This book is based on a course of lectures on fluid mechanics, which was given at the Department of Mathematics, University of California, Berkeley. Its goal is to present the basic ideas of fluid mechanics in a mathematically attractive form, as well as to consider the physical foundations of some constructions currently used for the analytical and numerical solution of the Navier-Stokes equations and hyperbolic systems of equations. The book is written in a lively and accessible language, which makes it possible to interest students in this rather complex subject.