Many efforts to detect Earth-like planets around low-mass stars are currently devoted to almost every extra-solar planet search. M dwarfs stand as ideal targets for Doppler radial velocity searches as their low masses and luminosities make low-mass planets orbiting within their habitable zones more easily detectable than those around higher-mass stars. Nonetheless, the statistics of the frequency of this kind of planet hosted by low-mass stars remains poorly constrained. Our M-dwarf radial velocity monitoring with HARPS-N within the HARPS-N Red Dwarf Exoplanet Survey Radial Velocity (HADES) project started in 2012 and is contributing to the widening of the current statistics through the in-depth analysis of accurate radial velocity observations in a narrow range of spectral sub-types from M0 to M3, to investigate the planetary population around a well-defined class of host stars. The HADES project is the result of a collaborative effort between the Italian Global Architecture of Planetary Systems (GAPS) Consortium, the Institut de Ciències de l’Espai de Catalunya (ICE), and the Instituto de Astrofísica de Canarias (IAC).