The article is divided in 2 parts. In the 1st part (PART I), we emit the hypothesis that a substance, called ether-substance, fills and constitutes all what is called “vacuum” in the Universe. We assume that it has a mass and consequently it could be the nature of dark matter. Modeling it as an ideal gas, we obtain the flat rotation curve of spiral galaxies. Using a very simple model of thermal transfer between baryonic particles and ether-substance, we obtain the baryonic Tully-Fisher’s law. Then we emit the hypothesis of the existence at every point of the Universe, of a particular Referential called “local Ether”. We will see that both previous concepts of ether can be detected experimentally. So we will call “Cosmology based on ether” (CBE) Cosmology based on the previous concepts of ether. In this CBE, topology of the Universe is much simpler than topologies obtained by the Standard Cosmological model (SCM), in particular in the 1st model. Indeed, contrary to MSC, the 1st model of CBE does not need dark energy nor Cosmological constant, nor complicated mathematics based on General Relativity. Nonetheless, it permits to obtain a very simple Hubble’s constant, in 1/t, t age of the Universe, and to predict the different cosmological distances in agreement with observation. CBE permits also to interpret, contrary to MSC, the Referential in which fossil radiation is isotropic. Nonetheless, CBE remains compatible with Special and General Relativity. In the 2nd part (PART II) we will study some problems raised by PART I (motion of galaxies inside the intergalactic ether-substance, concentration of ether-substance around stars..)