This course offers an introduction to the concepts underlying nonlinear optical phenomena. Topics include: Basic formalism and classification of nonlinear optical processes through the framework of nonlinear susceptibilities: Non-phase-matched processes (e.g., rectification, Kerr effect, soliton generation, Pockels effect, two-photon absorption, degenerate four-wave mixing); phase-matched processes (parametric conversion, harmonic and difference frequency generation); Raman and Brillouin scattering. Microscopic (quantum) origin of nonlinear susceptibilities, and the use of nonlinear optics to generate nonclassical states of light. Connections between the classical and quantum regimes.