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 (mSR) techniques, this book combines for the first time a detailed discussion of the physical information contained in the measured polarization 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 mSR 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.About the Author: Alain Yaouanc graduated from the University Joseph Fourier of Grenoble, France, in 1982. During his studies he spent about one year at CERN (Geneva, Switzerland). After his PhD, he spent one year as a postdoctoral scientist in the group of Bob Heffner at Los Alamos National Laboratory (USA). This group was involved in the investigation of condensed matter using positive muon spin rotation and relaxation techniques. Since 1983 he has been working as a physicist at the Commissariat a l'Energie Atomique (CEA) in Grenoble. Pierre Dalmas de Reotier took his PhD at the Centre d''Etudes Nucleaires de Grenoble in 1990. In 1991 he took up a Post-doctoral fellowship from the Alexander von Humboldt Foundation, studying spin dynamics in intermetallic systems at the Hahn-Meitner Institute in Berlin. Since 1992 he has been a Researcher at CEA Grenoble, and took his Habilitation diploma from University Joseph Fourier (Grenoble) in 2006.