Strings in cosmological spacetimes and their back-reaction

This is a short review on strings in curved spacetimes. We start by recalling the classical and quantum string behaviour in singular plane waves backgrounds. We then report on the string behaviour in cosmological spacetimes (FRW, de Sitter, power inflation) which is by now largerly understood. Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is considered as source of the spacetime geometry. The string equation of state is determined from the behaviour of the explicit string solutions. This yields a self-consistent cosmological solution exhibiting realistic matter dominated behaviour R \sim (T)^{2/3}\; for large times and radiation dominated behaviour R \sim (T)^{1/2}\; for early times. Inflation in the string theory context is discussed