  We define string geometry: spaces of superstrings including the interactions,
their topologies, charts, and metrics. Trajectories in asymptotic processes on
a space of strings reproduce the right moduli space of the super Riemann
surfaces in a target manifold. Based on the string geometry, we define
Einstein-Hilbert action coupled with gauge fields, and formulate superstring
theory non-perturbatively by summing over metrics and the gauge fields on the
spaces of strings. This theory does not depend on backgrounds. The theory has a
supersymmetry as a part of the diffeomorphisms symmetry on the superstring
manifolds. We derive the all-order perturbative scattering amplitudes that
possess the super moduli in type IIA, type IIB and SO(32) type I superstring
theories from the single theory, by considering fluctuations around fixed
backgrounds representing type IIA, type IIB and SO(32) type I perturbative
vacua, respectively. The theory predicts that we can see a string if we
microscopically observe not only a particle but also a point in the space-time.
That is, this theory unifies particles and the space-time.
