In this lecture we address the following issues in the context of string
theories: i) The role played by S and T dualities in obtaining topological
inflation in N=1 supergravity models, ii) A mechanism to generate the baryon
asymmetry of the Universe based on the string interactions that violate CPT
symmetry and iii) The quantum cosmology of the dimensionally reduced
multidimensional Einstein-Yang-Mills system.Comment: Latex file plus macro espcrc2.sty and two figures. Invited talk
presented at the Second Conference on Constrained Dynamics and Quantum
Gravity, Santa Margherita Ligure, Italy, September 1996. To appear in Nucl.
Phys. B. Supp
