Primarily intended for postgraduate students and researchers in the fields of condensed matter science, chemical physics and material science, who plan to use the muon spin rotation, relaxation amd resonance (#uSR) techniques, this book combines for the first time a detailed discussion of the physical information contained in the measured polarisation functions with real-life examples taken from the literature. It is divided in three main parts. The first part presents some typical results of the application of #uSR and explains the basic principles involved. The second part is the core of this book. It presents a comprehensive discussion of the measured polarisation functions. In the third part we analyse in four chapters selected examples taken from the following fields: diffusion properties of muon and muonium, magnetism, superconductivity, and muonium centres in materials. The book is completed by an epilogue and eight appendices.