  Recent progress in the preheating phenomena for inflationary cosmology is
reviewed. We first discuss estimates of the preheating time scale and particle
production at the early stages of parametric amplification within the Mathieu
and Lam'e approximations and we analyze their precision and limitations. The
necessity of self-consistent calculations including the non-linearity of the
field theory equations in an energy conserving scheme is stressed. The large N
calculations including the field back-reaction are reviewed. For spontaneously
broken theories the issue of symmetry restoration is analyzed. A discussion of
the possibility and criterion for symmetry restoration is presented.
