This dissertation details the development and experimental implementation of single-photon atomic cooling. In this scheme atoms are transferred from a large-volume magnetic trap into a small-volume optical trap via a single spontaneous Raman transition that is driven near each atom's classical turning point. This arrangement removes nearly all of an atomic ensemble's kinetic energy in one dimension. This method does not rely on a transfer of momentum from photon to atom to cool. Rather, single-photon atomic cooling achieves a reduction in temperature and an increase in the phase-space density of an atomic ensemble by the direct reduction of the system's entropy. Presented here is the application of this technique to a sample of magnetically trapped ⁸⁷Rb. Transfer efficiencies between traps of up to 2.2% are demonstrated. It is shown that transfer efficiency can be traded for increased phase-space compression. By doing so, the phase-space density of a magnetically trapped ensemble is increased by a factor of 350 by the single-photon atomic cooling process. / text