Nonreciprocity -- the change in transmission amplitudes under the exchange of source and detector -- is a useful property in both the classical and quantum world. This thesis builds the theory for a nonreciprocal microwave system using the quantum properties of rare earth doped crystals. These crystals are promising platforms for a variety of quantum research, such as transduction and memory, and it is possible that nonreciprocity could be useful in that research. We begin by developing the background knowledge of nonreciprocity, microwave cavities in quantum physics, and rare earth doped crystals necessary to build up this theory. Then, we tackle the theory of the system, showing how a dissipative interaction between a microwave cavity and a rare earth doped crystal leads to nonreciprocal transmission amplitudes. With the theory developed we turn to the experimental side. We see the design and procurement process for the specific kind of cross resonator used for the nonreciprocal system, and then the setup used to measure the transmission amplitudes in a dilution refrigerator. Finally, we see the preliminary results of these measurements and discuss next steps to improve the observed nonreciprocity.