We discuss some aspects of string cosmology with an emphasis on the role
played by the dilaton.
A cosmological scenario based on the assumption that all spatial dimensions
are periodic so that winding modes play an important role is reviewed. A
possibility of a transition from a `string phase' to the `standard' cosmology
via a radiation dominated era and inflation is analysed. We also summarise some
recent results about time dependent solutions of tree level string equations.Comment: 30 pages, DAMTP-92-36, harvma
