An exploratory study of the cosmology of moduli in string theory. Moduli are argued to be natural inflaton fields and lead to a robust inflationary cosmology in which inflation takes place at the top of domain walls. The amplitude of microwave background fluctuations constrains the dynamics responsible for inflation to take place at a higher scale than supersymmetry breaking. Models explaining this difference in scales and also preventing the dilaton from running to infinity are proposed. The problem of dilaton domination of the energy density of the universe is not resolved.

harvmac, 37 pages, 3 figures as a separate uuencoded tar file