Fluid mechanics is often thought of as a branch of engineering, but it is in fact a lively and deep part of theoretical physics. Ideas that arose in more modern areas of physics (general relativity or high energy physics) can be applied to explain and better understand this ancient subject. This is necessary in order to train the next generation of theoretical physicists to attack some of the oldest unsolved problems of physics: turbulence and dynamical
instabilities. In this book, the basic principles are explained and applied to several branches of fluid mechanics: boundary layers, shocks, instabilities. The book connects different
approaches to fluid mechanics, with three chapters on numerical methods, analysis of Navier-Stokers equations (Leray), two chapters on chaos (Smale's and Aref's theories), and two on Hamiltonian methods. Renormalization, an advanced idea of physics, is explained without assuming any knowledge of quantum theory.