  Exact superstring solutions are constructed in 4-D space-time, with positive
curvature and non-trivial dilaton and antisymmetric tensor fields. The full
spectrum of string excitations is derived as a function of moduli fields
$T^{i}$ and the scale $\mu^2=1/(k+2)$ which is induced by the non-zero
background fields. The spectrum of string excitations has a non-zero mass gap
$\mu^2$ and in the weak curvature limit ($\mu$ small) $\mu^2$ plays the role of
a well defined infrared regulator, consistent with modular invariance, gauge
invariance, supersymmetry and chirality.
  The effects of a covariantly constant (chomo)magnetic field $H$ as well as
additional curvature can be derived exactly up to one string-loop level. Thus,
the one-loop corrections to all couplings (gravitational, gauge and Yukawas)
are unambiguously computed and are finite both in the UltraViolet and the
InfraRed regime. These corrections are necessary for quantitative string
superunification predictions at low energies. The one-loop corrections to the
couplings are also found to satisfy Infrared Flow Equations. Having in our
disposal an exact description which goes beyond the leading order in the
$\alpha'$-expansion or the linearized approximation in the magnetic field, we
find interesting clues about the physics of string theory in strong
gravitational and magnetic fields. In particular, the nature of gravitational
or magnetic instabilities is studied.
