  The Einstein-Hilbert Lagrangian for gravity is non-renormalizable at loop
level. However, it can be treated in the effective field theory framework which
means that gravity as an effective theory can be renormalized when a proper
expansion of the effective Lagrangian is made. At the same time, the Feynman
rules for gravity are very complicated, although the resulting amplitudes do
not have the same complications. Therefore, in this thesis we want to simplify
the Feynman rules as much as possible by using the most general parameterized
gauge condition, adding all possible parameterized total derivative terms and
redefining the gravitational, ghosts and scalar fields in a general
parameterization way. By choosing the parameters in a specific way, we obtain
simplified Feynman rules, especially the triple and quadruple graviton vertices
are simplified. In addition, we verify our simplified rules by calculating the
amplitudes of scalar-graviton and graviton-graviton scattering at tree level
using the simplified and standard Feynman rules. Finally, we show the utility
of these simplified rules by calculating some one-loop diagrams for
scalar-graviton scattering and comparing to the standard Feynman rules.
