An international collaboration has grown around the project of Microcalorimeter Arrays for a Rhenium Experiment (MARE) for a direct and calorimetric measurement of the electron antineutrino mass with sub‐electronvolt sensitivity.MARE is divided into two phases. The first phase (MARE‐1) consists of two independent experiments using the presently available detector technology to reach a sensitivity of mv⩽2eV/c2. The goal of the second phase (MARE‐2) is to achieve a sub‐electronvolt sensitivity on the neutrino mass.The Milan MARE‐1 experiment is based on arrays of silicon implanted microcalorimeters, produced by NASA/GSFC, with dielectric silver perrhenate absorbers, AgReO4. We present here the status of MARE‐1 in Milan which is starting data taking with 2 arrays (72 detectors). In this configuration a sensitivity of about 5 eV can be achieved in two years. We describe in details the experimental setup which is designed to host up to 8 arrays (288 detectors). With 8 arrays, two years of measurement would imp...