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Experiments with muons (μ+) and muonium atoms (μ+e−) offer several promising possibilities for testing fundamental symmetries. Examples of such experiments include the search for a muon electric dipole moment, measurement of the muon g − 2 and experiments with muonium from laser spectroscopy to gravity experiments. These experiments require high quality muon beams with small transverse size and high intensity at low energy. At the Paul Scherrer Institute, Switzerland, we are developing a novel device that reduces the phase space of a standard μ+ beam by a factor of 1010 with 10− 3 efficiency. The phase space compression is achieved by stopping a standard μ+ beam in cryogenic helium gas. The stopped μ+ are manipulated into a small spot using complex electric and magnetic fields in combination with gas density gradients. From there, the muons are extracted into the vacuum and into a field-free region. Various aspects of this compression scheme have been demonstrated. In this article the current status will be reported. [ABSTRACT FROM AUTHOR]