This is an account of the construction and finiteness analysis of multi-loop scattering amplitudes for superstrings, and of the guarantee that for certain superstrings (in particular the heterotic one), the symmetries of the theory in the embedding space-time are those of the super-poincare group, SP10 and that the multi-loop amplitudes are each finite. The book attempts to be self-contained in its analysis, although it draws on the works of many researchers. It also presents a complete field theory for such superstrings. As such it demonstrates that gravity can be quantized satisfactorily by superstrings.