  In this paper we will look at the phenomenon of Microwave Amplification by
Stimulated Emission of Radiation (a maser system). We begin by deriving
amplification by stimulated emission using time-dependent perturbation theory,
in which the perturbation provided by external radiation. When this
perturbation is applied to an ensemble of particles exhibiting a population
inversion, the result is stimulated microwave radiation. We will explore both
unsaturated and saturated masers and compare their properties. By understanding
their gain, as well as the effect of line broadening, astronomers are to
identify astrophysical masers. By studying such masers, we gain new insight
into poorly understood physical environments, particularly those around young
and old stars, and compact stellar bodies.
