In 2010 we started a spectroscopic survey to obtain visible and near-infrared spectra of primitive asteroids in the main belt. The main objective was to characterize the collisional families located in the inner part of the belt, and believed to be the origin of primitive near-Earth asteroids, in particular those that are the targets of two sample-return missions (OSIRIS-REx and Hayabusa2). Now we have extended this survey, called PRIMitive Asteroids Spectroscopic Survey (PRIMASS) to observe other families of primitive asteroids in the rest of the belt, as well as groups like the Cybeles or Hildas. We have created a library that contains all the obtained spectra (PRIMASS-L) and that we intend to make available to all the planetary science community.