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 off-shell string amplitudes and of nonperturbative type IB states. We conclude with analysis of the equilibrium thermodynamics of free strings establishing the absence of the Hagedorn phase transition. We show that both of the 10D heterotic strings have a stable finite temperature ground state with gauge group SO(16) * SO(16). The free energy at the Kosterlitz-Thouless phase transition is minimized with finite entropy and positive specific heat.
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