Muon science is assuming a central role in scientific and technological studies of the solid state within the disciplines of physics, chemistry and materials science. This text is a collection of lectures delivered at SUSSP 51, the aim of which is to formalize and publicize key developments in both theoretical and experimental aspects of muon spin relaxation, rotation and resonance. The contributors are experts in muon instrumentation and applications of muon science, who cover topics which include: muon production; beamlines and instrumentation; muonium chemistry; muon catalysed fusion; fundamental muon physics; ultra-cold muons; magnetism; superconductivity; diffusion; semiconductors; simulations; and data analysis. The book assumes no prior expertise in muon science and takes the reader through from introductory material to developments in the field. Consistent notation and nomenclature are maintained throughout, with cross-referencing to both new and experienced muon beam scientists wishing to develop their knowledge and understanding of the subject.