We present the main features of a home-built scanning tunneling microscope that has been attached to the mixing chamber of a dilution refrigerator. It allows scanning tunneling microscopy and spectroscopy measurements down to the base temperature of the cryostat, T approx. 30mK, and in applied magnetic fields up to 13T. The topography of both highly-ordered pyrolytic graphite (HOPG) and the dichalcogenide superconductor NbSe2 have been imaged with atomic resolution down to T approx. 50mK as determined from a resistance thermometer adjacent to the sample. As a test for a successful operation in magnetic fields, the flux-line lattice of superconducting NbSe2 in low magnetic fields has been studied. The lattice constant of the Abrikosov lattice shows the expected field dependence B^{-0.5} and measurements in the STS mode clearly show the superconductive density of states with Andreev bound states in the vortex core.
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