This article reviews the present status of the challenging field of muon catalysed fusion, by which fusion of light nuclei can be catalysed at low temperatures by muon binding. The study of this intriguing phenomenon encompasses different disciplines of physics, including particle, nuclear, atomic, molecular, accelerator and reactor physics. Starting with the intrinsic characteristics of the muon, the review highlights the physics of the negative muon in matter that culminates in the fusion act. The post-fusion scenario and the dynamics of the reactions and associated physics are considered. In part II, the applicational and utilisation prospects and experimental status are discussed
