This book describes the fundamental aspects of nonlinear optics from basic principles to applications. Starting from the polarization induced by an electric field in a material, it relates the induced polarization to the propagating fields. It describes the properties of the induced polarization through a material response expressed both in the time and frequency domains leading to the nonlinear wave equation. The second part of the book focuses on applications of nonlinear interaction between light and matter, and considers nonlinearities in crystals and optical fibers.