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 (µSR) 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 µSR 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.