  We explain how perturbative string theory can be viewed as an exactly
renormalizable Weyl invariant quantum mechanics in the worldsheet
representation clarifying why string scattering amplitudes are both finite and
unambiguously normalized and explaining the origin of UV-IR relations in
spacetime. As applications we examine the worldsheet representation of
nonperturbative type IB states and of string solitons. We conclude with an
analysis of the thermodynamics of a free closed string gas establishing the
absence of the Hagedorn phase transition. We show that the 10D heterotic
strings share a stable finite temperature ground state with gauge group
SO(16)xSO(16). The free energy at the self-dual Kosterlitz-Thouless phase
transition is minimized with finite entropy and positive specific heat. The
open and closed string gas transitions to a confining long string phase at a
temperature at or below the string scale in the presence of an external
electric field.
