Fourier analysis and nonlinear partial differential equations Recent years have seen a growth in interest in using partial differential equations in methods of Fourier analysis. This monograph sets out state of the art models of these techniques as applied to transport heat wave and Schrodinger equations. Basic analysisLittlewood Paley theory Transport and transport diffusion equations Quasilinear symmetric systems The incompressibile Navier Stokes system Anisotropic viscosity Euler system for perfect incompressible fluids Strichartz estimates and applications to semilinear dispersive equations Smoothing effect in quasilinear wave equations The compressible Navier Stokes system.