  The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that
establishes a relation between loop-level and tree-level scattering amplitudes.
This is achieved by directly applying the Residue Theorem to the
loop-energy-integration. The result is a sum over all possible single cuts of
the Feynman diagram in consideration integrated over a modified phase space.
These single-cut integrals, called Dual contributions, are in fact tree-level
objects and thus give rise to the opportunity of bringing loop- and
tree-contributions together, treating them simultaneously in a common Monte
Carlo event generator. Initially introduced for one-loop scalar integrals, the
applicability of the LTD has been expanded ever since. In this thesis, we show
how to deal with Feynman graphs beyond simple poles by taking advantage of
Integration By Parts (IBP) relations. Furthermore, we investigate the
cancellation of singularities among Dual contributions as well as between real
and virtual corrections. For the first time, a numerical implementation of the
LTD was done in the form of a computer program that calculates one-loop
scattering diagrams. We present details on the contour deformation employed
alongside the results for scalar integrals up to the pentagon- and tensor
integrals up to the hexagon-level.
