From the microscopic to the macroscopic world: from nucleons to neutron stars

Recent observations of neutron-star properties, in particular the recent detection of gravitational waves emitted from binary neutron stars, GW 170817, open the way to put strong constraints on nuclear interactions. In this paper, we review the state of the art in calculating the equation of state of strongly interacting matter from first principle calculations starting from microscopic interactions among nucleons. We then review selected properties of neutron stars that can be directly compared with present and future observations.