Muon physics possibilities at a muon-neutrino factory

New intense proton accelerators with above GeV energies and MW beam power, such as they are discussed in connection with neutrino factories, appear to be excellently suited for feeding bright muon sources for low-energy muon science. Muon rates with several orders of magnitude increased flux compared to present facilities will become available. This will allow higher precision in experiments which were statistics limited so far such as searches for rare decays, muonium spectroscopy, muon capture, muon catalyzed fusion, muon decay studies and measurements muon moments and parameters. Novel and most important experiments will become possible. For example a permanent electric dipole moment (edm(mu)) of a muon could be searched with by far unprecedented accuracy and with a physics potential well beyond the possibilities of present electron, neutron and nuclear edm searches. Investigations of short lived radioactive nuclei using muonic atom spectroscopy would become feasible.