This thesis considers aspects of parametric conversion of Mossbauer gamma rays. This process is important because it could be used to tune the output of a gamma ray laser; but, furthermore, it is a process of fundamental intrinsic interest in quantum electrodynamics. We first calculate the S matrix for the parametric process and obtain from this the differential cross section. We then discuss the signal sharpening which occurs for coherent parametric conversion near a Bragg angle and, finally, make a specific calculation of the expected counting rate from a crystal of Ytterbium 171.