In this thesis next-to-leading order mixed QCD-electroweak corrections to the Higgs boson gluon-fusion cross section are evaluated. Leading order and virtual next-to-leading order amplitudes are expressed in terms of two- and three-loop master integrals. These integrals are evaluated using differential equations augmented by the choice of a basis of uniformly transcendental functions. The integration constants are fixed in a systematic way by numerically matching the solutions to their large-mass expansion. The analytic results for the master integrals are expressed in terms of uniformly transcendental combinations of Goncharov polylogarithms. The real emission contributions are implemented using the soft-gluon approximation. The evaluation of the cross section shows that the ratio between QCD and mixed QCD-electroweak contributions to the cross section remains nearly unchanged from leading order to next-to-leading order. This result removes one of the important uncertainties if the Higgs boson gluon fusion cross section.