  At the end of the inflationary stage of the early universe, profuse particle
production leads to the reheating of the universe. Such explosive particle
production is due to parametric amplification of quantum fluctuations for the
unbroken symmetry case (appropriate for chaotic inflation), or spinodal
instabilities in the broken symmetry phase(which is the case in new inflation).
The self-consistent methods presented in these lectures are the only
approaches, so far, that lead to reliable quantitative results on the reheating
mechanism in the inflationary universe. They fully use the field theoretical
Schwinger-Keldysh out of equilibrium method in a non-perturbative way. These
approaches take into account the non-linear interaction between the quantum
modes and exactly conserve energy (covariantly). Simplified analysis that do
not include the full backreaction and do not conserve energy, result in unbound
particle production and lead to quantitatively erroneous results. For
spontaneously broken theories the issue of whether the symmetry may be restored
or not by the quantum fluctuations is analyzed. The precise criterion for
symmetry restoration is presented. The field dynamics is symmetric when the
energy density in the initial state is larger than the top of the tree level
potential. When the initial energy density is below the top of the tree level
potential, the symmetry is broken.
