This thesis reports on recent results which pave the way for future experiments in the emerging field of quantum magnonics. Chapter 1 presents a brief outline of the field of magnonics, which provides the context in which quantum magnonics has begun to develop. Chapter 2 provides an introduction to the theory of spin waves, which is necessary to understand the experiments reported in the thesis. In Chapter 3, the experimental methods and materials used to carry out the investigations in the thesis are described. Chapter 4 describes the coupling of resonant magnon modes in a sphere of yttrium-iron garnet to photon modes in a coplanar-waveguide resonator. Strong coupling is achieved to multiple magnon modes, and a theoretical model is used to identify the magnon modes which couple most strongly to the photon mode. In Chapter 5, the behaviour of propagating magnon modes is investigated in a waveguide formed from a thin film of yttrium-iron garnet. Two different configurations are investigated supporting different types of propagating mode, namely backward-volume and surface spin waves. Simulations are performed which reproduce the main features of the data. Chapter 6 characterises the effect of the gadolinium-gallium garnet substrate on propagating spin waves. The magnitude of this effect is dependent on both the orientation and temperature of the sample. Finally, Chapter 7 provides a short summary of the results of the thesis, and speculates on how they may inform future work in the field.