  The big bang model and the history of the early universe according to the
grand unified theories are introduced. The shortcomings of big bang are
discussed together with their resolution by inflationary cosmology. Inflation,
the subsequent oscillation and decay of the inflaton, and the resulting
"reheating" of the universe are studied. The density perturbations produced by
inflation and the temperature fluctuations of the cosmic background radiation
are discussed. The hybrid inflationary model is described. Two "natural"
extensions of this model which avoid the disaster encountered in its standard
realization from the overproduction of monopoles are presented. Successful
"reheating" satisfying the gravitino constraint takes place after the end of
inflation in all three versions of hybrid inflation. Adequate baryogenesis via
a primordial leptogenesis occurs consistently with the solar and atmospheric
neutrino oscillation data. The primordial lepton asymmetry is turned partly
into baryon asymmetry via the sphalerons which are summarized.
