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Quantization of Free Fields: The non-interacting field belonging to a new{\bf SO(1,3)\/} gauge field theory equivalent to General Relativity iscanonically quantized in the Lorentz gauge and the physical Fock space for freegauge particles is constructed. To assure both relativistic covariance andpositivity of the norm and energy expectation value for physical statesrestrictions needed in the construction of the physical Fock space are putconsequentially on state vectors, and not on the algebra of creation andannihilation operators as usual - alltogether providing the second step inconsistently quantizing gravitation  Proof of Renormalizability: A new SO(1,3) gauge field theory classicallyequivalent to General Relativity is quantized and the gauge-fixed path integralrepresentation of the quantum effective action (QEA) is derived. Both thegauge-fixed classical action and the QEA are shown to be invariant undernilpotent BRST variations of the gauge, matter, ghost, antighost andNakanishi-Lautrup fields defining the theory and a Zinn-Justin equationconstraining the QEA is derived. Dimensional analysis and the various linearconstraints put on the QEA plus the ones from the non-linear Zinn-Justinequation are deployed to demonstrate full renormalizability such that allinfinities appearing in a perturbative expansion of the QEA can be absorbedinto the gauge-fixed classical action solely by field renormalizations andcoupling redefinitions - alltogether providing the third step in consistentlyquantizing gravitation

The Quantum Theory of Gravitation: I Quantization of Free Fields - II Proof of Renormalizability