The basis of this dissertation is a review of the quantum mechanical formulation of damping and stimulation, particularly in non-linear optical processes. The basic problems of the quantum theory of damping are discussed, and the formalism for the quantum theory is introduced. The study of a particular example, that of a damped simple harmonic oscillator, provides an introduction to the handling of the basic tool, the master equation. The physical aspects of the non-linear processes are contained in the systems' photon statistics, and the master equation provides several approaches for obtaining these. This theory is then used to formulate a quantum mechanical model of Raman scattering by phonons, and to thus obtain the photon statistics of the scattered radiation.