In this manuscript we do the Quantum Field Theory (QFT) of Einstein's Gravity (EG) based on the developments previously made by Suraj N. Gupta and Richard P. Feynman, using a new and more general mathematical theory based on Ultrahyperfunctions \cite{ss} \\ \nd Ultrahyperfunctions (UHF) are the generalization and extension to the complex plane of Schwartz 'tempered distributions. This manuscript is an {\bf application} to Einstein's Gravity (EG) of the mathematical theory developed by Bollini et al \cite{br1, br2, br3, br4} and continued for more than 25 years by one of the authors of this paper. A simplified version of these results was given in \cite{pr2} and, based on them, (restricted to Lorentz Invariant distributions) QFT of EG \cite{pr1} was obtained. We will quantize EG using the {\bf most general quantization approach}, the Schwinger-Feynman variational principle \cite{vis}, which is more appropriate and rigorous than the popular functional integral method (FIM). FIM is not applicable here because our Lagrangian contains derivative couplings. \\ \nd We use the Einstein Lagrangian as obtained by Gupta \cite{g1,g2,g3}, but we added a new constraint to the theory. Thus the problem of lack of unitarity for the $S$ matrix that appears in the procedures of Gupta and Feynman.\\ \nd Furthermore, we considerably simplify the handling of constraints, eliminating the need to appeal to ghosts for guarantying unitarity of the theory. \\ \nd Our theory is obviously non-renormalizable. However, this inconvenience is solved by resorting to the theory developed by Bollini et al. \cite{br1,br2,br3,br4,pr2}\\ \nd This theory is based on the thesis of Alexander Grothendieck \cite{gro} and on the theory of Ultrahyperfunctions of Jose Sebastiao e Silva \cite{ss} \\ Based on these papers, a complete theory has been constructed for 25 years that is able to quantize non-renormalizable Field Theories (FT). \\ Because we are using a Gupta-Feynman based EG Lagrangian and to the new mathematical theory we have avoided the use of ghosts, as we have already mentioned, to obtain a unitary QFT of EG