  The hypothesis that the Universe underwent a period of exponential expansion
at very early times has become the most popular theory of the early Universe.
Not only does it solve some of the problems of standard big bang cosmology, but
it also provides a causal theory for the origin of primordial density
fluctuations which may explain the observed density inhomogeneities and cosmic
microwave fluctuations in the Universe. In these lectures, a review of the
basic principles of inflationary cosmology is given, focusing on the theory of
the origin and growth of cosmological perturbations. The lectures also focus on
some recent progress in inflationary cosmology (in particular on an improved
theory of reheating), and on several problems with the present inflationary
Universe models. A couple of possible approaches to resolve these issues are
suggested.
