The relativistic universe -- The Friedmann models -- Alternative cosmologies : past and present -- Observational properties of the universe -- Physical properties of the Hot Big Bang -- The Big Bang and quantum gravity -- Phase transitions and inflation -- The hadron and lepton eras -- The plasma era -- Introduction to Jeans theory -- Jeans instability in Friedmann models -- The origin of structure I : baryons only -- The origin of structure II : non-baryonic matter -- Cosmological perturbations -- Non-linear evolution of perturbations -- Statistics of galaxy clustering -- The cosmic microwave background -- Peculiar motions of galaxies -- The post-recombination universe.