Non-linear optics (NLO) is the branch of optics that describes the behaviour of light in non-linear media, that is, media in which the dielectric polarisation P responds nonlinearly to the electric field E of the light. This nonlinearly is typically only observed at very high light intensities such as those provided by pulsed lasers. Non-linear optics is of considerable research interest since it includes: Free space and guided wave non-linear optics; Weak (second and third order etc. effects) and strong (non-perturbative)nonlinearities; Fast (electronic fs timescale)and slow (thermal ms timescale) non-linearities; Novel non-linear materials; Numerical simulation of non-linear optical propagation; Applications of non-linear optics in fields such as signal processing, optical communications, holographic memory and soliton phenomena. This Advanced book provides the latest research from around the globe in this fast-moving field.