The use of positive muons to simulate protons in solids is a relatively new, but already successful field of research, which exploits the unique properties of the muon. This book is a collection of papers for special issues of the Philosophical Magazine Part B and the Philosophical Magazine Transactions A, together with previously unreleased material presented at a seminar on the subject. The 30 papers here are written by an international team of experts who effectively cover both the theoretical and experimental aspects of the subject.