The muon is one of the elementary particles called leptons. The muon is the lightest unstable elementary particle and has a relatively long lifetime compared to the other elementary particles. Furthermore, a positively charged muon behaves like a light proton (1/9 of the proton mass), and a negatively charged muon does like a heavy electron (200 times the electron mass) in materials. Therefore, the muon is known to be a unique tool to study in various science fields, from elementary particle physics, materials science to application. Potential science that can be explored with muons will be mentioned. Particular emphasis will be given to our planned muon particle physics experiment "COMET" at J-PARC. And also some development on a muon beam source at Osaka University, called the MuSIC project, will be mentioned. The talk will be given as introductory to the level of undergraduate students.