The discovery of the Higgs boson has fully confirmed the Standard Model of particles and fields. Nevertheless, there are still fundamental phenomena, like the existence of dark matter and the baryon asymmetry of the Universe, deserving an explanation that could come from the discovery of new particles. Searches for new physics with accelerators are performed at the LHC, looking for high massive particles coupled to matter with ordinary strength. A new experiment at CERN meant to search for very weakly coupled particles in the few GeV mass domain has been recently proposed. The existence of such particles, foreseen in different theoretical models beyond the Standard Model, is largely unexplored. A beam dump facility using high intensity 400 GeV protons is a copious source of such unknown particles in the GeV mass range. The beam dump is also a copious source of neutrinos and in particular it is an ideal source of tau neutrinos, the less known particle in the Standard Model. The neutrino detector can also search for dark matter through its scattering off the electrons. We report the physics potential of the SHiP experiment.