The standard model of Hot Big Bang can be summarized in a few lines.

Approximately fifteen billion years ago, the universe was born from a violent explosion. The primordial universe was at a very high temperature, higher than 10^13 Kelvin degrees. To 1/100 of second, the universe, with very high density and very high temperature (10 ^11 Kelvin degrees), consisted of an undifferentiated soup of matter and light (photons, electrons and positrons, neutrinos and antineutrinos, protons and neutrons), dominated by radiations. Then, the temperature decreased very quickly with the expansion of the universe (Weinberg 1980).

After 3 minutes and 45 seconds, the temperature being sufficiently low, the cores of deuterium, and then of helium took shape. After 700.000 years, the temperature having fallen to several thousands from Kelvin degrees, the first atoms of hydrogen and light elements (deuterium 2H, helium 3H, helium 4H, lithium 7Li) could be formed.

The expansion going on, the galaxies and the stars appeared followed by the great structures of the universe (galaxies clusters, superclusters of galaxies, large walls, etc...). The heavier chemical elements occurred in stars.

The theory of inflation, worked out to solve a certain number of serious problems posed by the model of Hot Big Bang, is a prolongation of it but is also independent of it.

The standard model of Hot Big Bang rests on a certain number of principles, facts, assumptions, presupposed and consequences, that we can enumerate and that we will analyze: redshifts of the remote galaxies and the constant of Hubble Ho; the expansion of the universe, general relativity and the cosmological principle; the theory of inflation; the Cosmic Microwave Background Radiation; the primordial nucleosynthesis and the ratio baryons/photons at the beginning of Hot Big Bang; the age of the universe; great structures of the universe; critical density and the geometrical shape of the universe. The problems of the dark mass, the cosmological constant and quintessence can be added to it.