Abstract: The study of coherent nonlinear effects such as self-induced transparency, which cannot be described by expressing P as a low-order polynomial in E, should be considered as part of nonlinear optics. This chapter turns the attention mainly to some “low-order” nonlinear optical effects in which can characterize the polarization using only the first few terms of a power series in the electric field. It considers some general properties of nonlinear susceptibilities for different media. As in the example of self-focusing, it is straight forward to obtain a wave equation for the electric field produced by a nonlinear polarization. Efficient second-harmonic generation requires the pump and second-harmonic fields to somehow be phase matched. Parametric fluorescence in which a pump wave at v3 incident on a nonlinear crystal results in the spontaneous generation of signal and idler photons at v1 and v2 may be called spontaneous two-photon downconversion, or simply two-photon downconversion. Controlled Vocabulary Terms electric fields; fluorescence; nonlinear optical susceptibility; nonlinear optics; polarisation