This book provides a comprehensive introduction to muon spectroscopy, an experimental technique that is widely used in condensed matter physics and chemistry to study many different compounds, including semiconductors, magnets, superconductors, chemical reactions and battery materials. The book is designed to be suitable for beginning graduate students but also serve as a reference for more experienced researchers in the field. The key principles are illustrated by numerous practical examples of the application of the technique to different areas of science and there are many worked examples and problems provided to test understanding.