Our treatment of the quantum theory of radiation so far has predominantly involved entire systems, such as the electromagnetic field in a cavity. In most areas of quantum optics, however, we are interested in only part of the entire system. For example, in the laser problem, we want to know the field but are not particularly interested in what happens to the atoms. We find it convenient to separate the system of primary interest from that (or those) of secondary interest and to call the former simply the “system” and the latter the “res ervoir.” We can eliminate the reservoir by using the reduced density operator method in the Schrodinger (or interaction) picture or the noise operator method in the Heisenberg picture. In this chapter we discuss the density operator method, which provides computational convenience while stressing the statistical aspects of the problem. In Chap. 19 we use the noise operator approach, which often requires more calculation but offers a direct physical appeal in its resemblance to the classical Brownian motion problem.