  These lecture notes intend to form a short pedagogical introduction to
inflationary cosmology, highlighting selected areas of recent progress such as
reheating and the theory of cosmological perturbations. Problems of principle
for inflationary cosmology are pointed out, and some new attempts at solving
them are indicated, including a nonsingular Universe construction by means of
higher derivative terms in the gravitational action, and the study of
back-reaction of cosmological perturbations.
