I. INTRODUCTION II. SETUP Thirty years after the invention of the scanning tunneling microscope (STM) by Binnig and Rohrer [1] the interest in this technique is still increasing. STM and scanning tunnel- ing spectroscopy (STS) measurements on superconductors are one example of this emerging field. High-temperature superconductors have been successfully investigated by STM and STS [2, 3]. For the study of heavy-fermion superconductors with transitions temperatures of about 1 K and below, STM and STS measurements at very low temperatures are required. A STM operating at such low temperatures would make it feasible to investigate properties of unconventional superconductors, e. g., the order parameter in UPt 3 . To observe the full opening of the superconducting gap, the temperature has to be sufficiently below the critical temperature, e. g., T$_{c}$ ≈ 550 mK for UPt 3 [4]. In the last years, STMs for low temperatures down to 300 mK and moderate magnetic fields have become commercially available. However, for even lower temperatures and high magnetic fields B ≥ 10 T only a small number of home-built scan heads exist [5]. The im- plementation of an STM into a dilution refrigerator is not straightforward, there are several requirements in order to successfully run the system, i. e., mechanical and electrical noise damping, a functional coarse approach for low temperatures, etc. In this article we describe a home-built STM for low temperatures T ≈ 30 mK that works in a standard dilution refrigerator and in magnetic field up to B = 13 T. Calibration mea- surements on highly-ordered pyrolytic graphite (HOPG) and NbSe 2 at room temperature are presented. Calibration at low temperature and in magnetic fields has been performed on NbSe 2 in the Shubnikov phase. The measurements demonstrate the good spatial and energy resolution, respectively a high voltage resolution of the order of 1 K and stability of the instrument. The low-temperature STM has to meet several stringent requirements. First of all the setup has to be rigid enough to provide mechanical stability and a good thermal contact to the mixing chamber. The choice of appropriate materials for temperature- and field- dependent measurements should take into account the thermal expansion and the magnetic 2