  In this thesis, higher-order corrections to the perturbative expansions of
scattering amplitudes involving the Higgs boson in the framework of Quantum
Chromodynamics are evaluated, where we focus on processes that are mediated
through heavy-quark loops. First, we derive the third-order corrections to the
form factor describing the Yukawa coupling of a Higgs boson to a pair of bottom
quarks. Furthermore, we compute the two-loop corrections to the $H\to
Z\,\gamma$ decay width by retaining the full dependence on the internal quark
mass. Finally, we describe the calculation of the planar Master Integrals
relevant to the two-loop amplitude for Higgs-plus-jet production with full
quark mass dependence. We accomplish this by establishing a method to derive
series expansions from differential equations, since the set of Master
Integrals involves elliptic structures.
