  The muonium atom is the purely leptonic bound state of a positive muon and an
electron. It has a lifetime of 2.2 $\mu$s. 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 groun dstate 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.
