Georeges Lemaître is one of the founders of relativistic cosmology. To him we owe the first ever paper (1927) comparing predictions of a cosmological model, being a solution to Einstein’s equations, with red shifts of distant galaxies, and a daring idea called by him the Primeval Atom Hypothesis that was a predecessor of the present Big Bang model. Basing on this hypothesis he predicted that the early universe was filled with radiation, the remnants of which should now be detectable. Erroneously, however, he tried to identify it with cosmic rays. In his discussions with Einstein he defended the necessity of introducing cosmological constant and favoured a cosmological solution (with a positive cosmological constant) starting with the initial singularity and having a quasi-static period in the middle part of its evolution. It is exactly this solution that seems to be in the best agreement with the present observational data of the Ia type of supernovae. Lemaître’s Primeval Atom Hypothesis can also be regarded as an early attempt to include quantum effects into the physics of the superdense state in the beginning.