The physics potential of an intense source of low-energy muons is studied. Such a source is a necessary stage towards building the neutrino factories and muon colliders which are being considered at present. The CERN Neutrino Factory could deliver muon beams with intensities 3-4 orders of magnitude higher than available now, with large freedom in the choice of the time structure. Low-energy muon physics contributes to many fields of basic research, including rare muon decays, i.e., decays that do not conserve muon number, measurements of fundamental constants, the muon anomalous magnetic moment, determination of the Lorentz structure of the weak interaction, QED tests, CPT tests, proton and nuclear charge distributions (even for short-lived isotopes), and condensed matter physics. In studying the experimental programme, we analyse the present limitations, list the requirements on the new muon beams, and describe some ideas on how to implement these beam lines in a CERN neutrino factory complex.
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