The muonium atom is the purely leptonic bound state of a positive muon and an electron. It has a lifetime of 2.2 µs. The absence of any known internal structure provides for precision experiments to test fundamental physics theories and to determine accurate values of fundamental constants. In particular ground state hyperfine structure transitions can be measured by microwave spectroscopy to deliver the muon magnetic moment. The frequency of the 1s–2s transition in the hydrogen-like atom can be determined with laser spectroscopy to obtain the muon mass. With such measurements fundamental physical interactions, in particular quantum electrodynamics, can also be tested at highest precision. The results are important input parameters for experiments on the muon magnetic anomaly. The... simplicity of the atom enables further precise experiments, such as a search for muonium–antimuonium conversion for testing charged lepton number conservation and searches for possible antigravity of muons and dark matter.