  A positive muon ($\mu^+$) and an electron ($e^-$) form the the hydrogen-like
muonium atom ($M$=$\mu^+ e^-$). Since it consists of two leptonic particles
which are according to present knowledge point-like, accurate calculations of
its level energies can be performed in the framework of standard theory. In
particular, the theoretical description of this system is possible almost
exclusively by Quantum Electrodynamics (QED) which has been verified in various
very high precision experiments. Due to the close confinement of the bound
state the muonium atom renders in addition the possibility for sensitive
searches for electron--muon interactions not included in the standard model.
Such exotic processes could affect the energy of the quantum states at a level
of the same order of magnitude as the precision achievable in modern
spectroscopic experiments.Oscillations between muonium and antimuonium
($\bar{M}$=$\mu^- e^+$) would violate separate additive lepton number
conservation which is a purely empirical law.
