Elementary introduction to pre-big bang cosmology and to the relic graviton background

Elementary introduction to pre-big bang cosmology and to the relic graviton background- A self-contained introduction to string cosmology and, in particular, to the background of relic cosmic gravitons predicted in the context of the so-called "pre-big bang". The text is aimed at graduate and advanced undergraduate students, and based on notes for lectures held by M. Gasperini at two schools in 1997 and 1998.