This article introduces a novel model of dark matter, conceptualized as a new physical element — termed dark substance — which is not composed of classical particles. This dark substance is proposed to pervade the universe, constituting what is commonly regarded as the vacuum. By assigning simple physical properties to this dark substance, we provide a theoretical justification for the flat rotation curves observed in galaxies and the baryonic Tully-Fisher relation. Subsequently, we examine the potential distributions of dark matter within galaxies and galaxy clusters, along with the associated galaxy velocities in clusters, within the framework of our proposed dark matter theory. Furthermore, leveraging this new dark matter model, we propose a New Cosmological Model (NCM) of the Universe, which is finite and flat. The NCM comprises two distinct mathematical formulations. The first closely resembles the Standard Cosmological Model (ΛCDM), while clarifying the nature of dark matter and dark energy, and offering an interpretation of the CMB rest frame and cosmological time. The second mathematical model is significantly simpler than the SCM, yet yields theoretical predictions consistent with astronomical observations at sufficiently low redshifts. In the concluding sections, we demonstrate that both the proposed dark matter model and the NCM can interpret observations related to the primordial universe and the CMB power spectrum. Finally, we show that these two mathematical models can be utilized to address the Hubble tension, leading to the definition of a third mathematical framework, referred to as the Δ model. An earlier version of this work, lacking recent astronomical data and covering fewer topics (particularly concerning the ΛCDM model, primordial universe, CMB power spectrum, and Hubble tension), was published in an applied physics journal (DELORT 2018).