The early stages of the universe evolution are discussed according to the hot big bang model and the grand unified theories. The shortcomings of big bang are summarized and their resolution by inflationary cosmology is sketched. Cosmological inflation, the subsequent oscillation and decay of the inflaton field, and the resulting reheating of the universe are studied in some detail. The density perturbations produced by inflation and the temperature fluctuations of the cosmic microwave background radiation are introduced. Baryogenesis via non-thermal leptogenesis is analyzed and dark energy and matter in the universe are presented. Quantum gravity and string theory are very briefly introduced. The problem of initial conditions for inflation is discussed in the light of string theory and the
possibly detectable primordial gravity waves from inflation are mentioned.