  This article is an extension of the author's second master thesis [1]. It
aims to introduce to the theory of perturbatively quantized General Relativity
coupled to Spinor Electrodynamics, provide the results thereof and set the
notation to serve as a starting point for further research in this direction.
It includes the differential geometric and Hopf algebraic background, as well
as the corresponding Lagrange density and some renormalization theory. Then, a
particular problem in the renormalization of Quantum General Relativity coupled
to Quantum Electrodynamics is addressed and solved by a generalization of
Furry's Theorem. Next, the restricted combinatorial Green's functions for all
two-loop propagators and all one-loop divergent subgraphs thereof are
presented. Finally, relations between these one-loop restricted combinatorial
Green's functions necessary for multiplicative renormalization are discussed.
  Keywords: Quantum Field Theory; Quantum Gravity; Quantum General Relativity;
Quantum Electrodynamics; Perturbative Quantization; Hopf Algebraic
Renormalization
