Exact string solutions are presented, where moduli fields are varying with
time. They provide examples where a dynamical change of the topology of space
is occurring. Some other solutions give cosmological examples where some
dimensions are compactified dynamically or simulate pre-big bang type
scenarios. Some lessons are drawn concerning the region of validity of
effective theories and how they can be glued together, using stringy
information in the region where the geometry and topology are not well defined
from the low energy point of view. Other time dependent solutions are presented
where a hierarchy of scales is absent. Such solutions have dynamics which is
qualitatively different and resemble plane gravitational waves. Talk presented
by E. Kiritsis in the 2\`eme Journ\'ee Cosmologie, Observatoire de Paris, 2-4
June 1994.Comment: LaTeX, 28pp. CERN-TH.7328/9
