The interface of cosmology with string and M(illennium) theory

The purpose of this review is to discuss recent developments occurring at the interface of cosmology with string and M theory. We begin with a short review of 1980s string cosmology and the Brandenberger-Vafa mechanism for explaining space-time dimensionality. It is shown how this scenario has been modified to include the effects of p-brane gases in the early universe. We then introduce the Pre-Big-Bang scenario(PBB), Hofava-Witten heterotic M theory and the work of Lukas, Ovrut and Wald end with a discussion of large extra dimensions, the Randall-Sundrum model a World cosmologies.