The article proposes a new model of dark matter. According to this new model, dark matter is a substance, that is a new physical element not constituted of classical particles, called dark substance, filling the universe and constituting what is called emptiness. Assuming some very simple physical properties to this dark substance, we theoretically justify the flat rotation curve of galaxies and the baryonic Tully-Fisher’s law. We then study according to our new theory of dark matter the different possible distributions of dark matter in galaxies and in galaxy clusters, and the velocities of galaxies in galaxy clusters.Then using the new model of dark matter we are naturally led to propose a new cosmological model of Universe, finite and flat. This new cosmological model is divided in 2 different mathematical models. The first one is very close to Standard Cosmological Model (ΛCDM model), but gives the nature of dark matter and dark energy, interprets the CMB rest frame and the Cosmological time. The 2nd proposed mathematical model is mathematically much simpler than the SCM but we will see that its theoretical predictions agree with astronomical observations for z sufficiently low. But we will see that the 1st model, mathematically very close to SCM is the model in agreement with astronomical observations, among them the observed anisotropies of the CMB. A first version of this article, much less complete, has been published in a review of applied physics (DELORT 2018).