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,- 30 papers on the topic of muon implantation - an experimental technique to investigate the properties of solids. The papers cover both the theoretical and experimental aspects of the subject.