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The CRESST experiment is looking for non-baryonic particle dark matter via nuclear scattering in CaWO4. The simultaneous measurement of the heat and the scintillation light generated by an event in a CaWO4 single crystal is used to discriminate between electron and nuclear recoils thanks to their different light output. This allows an efficient suppression of the electron recoil background. The set-up consists of modules with a 300 g CaWO4 crystal mounted in a reflective housing together with a light detector. The heat signal is read out using a superconducting transition-edge sensor (TES) made of tungsten evaporated directly on to the crystal that is operated at a few mK. Currently the second phase of the experiment is being set up at the Laboratori Nazionali del Gran Sasso in which it is planned to run 33 detector modules providing a total target mass of 10 kg. First test runs with prototype detectors have been successfully performed.