The preparation of a report dealing with such a large domain is almost an impossible task. Because so many different questions, problems and expertises are assembled under the word “Cosmology”, my approach has been the following: first to divide this field in a somewhat arbitrary fashion into the following sections: very early universe – elementary particle and cosmology – early nucleosynthesiscosmological parameters (Hubble constant, deceleration parameter, cosmological constant) – large scale structures, intergalactic gas, missing mass – clusters of galaxies and intercluster gas – anisotropy of the black body radiation – formation of galaxies – quasars and their evolution – cosmological evolution of radiosources. I have then asked to the most knowledgeable specialists to review briefly each of these most important questions on which many excitinq and very new results have been obtained not only by the astrophysicists themselves but also by particle physicists, nuclear physicists, theoretical physicists, … This is why the reader will read in section 1 the report on primordial nucleosynthesis written by G. Steigman, in section 2 Anisotropy of the black body radiation by D.T. Wilkinson and E. Meichiorri, in section 3 Clusters of galaxies by 3. Einasto, in section 4 Galaxy formation by B.J.T. Jones, in section 5 Quasars and their evolution by M. Schmidt and in section 6 the Cosmological evolution of radio sources by R.A. Windhorst. Let me thank these colleagues for their excellent work in writing these various reviews.