  Top quark physics are an appropriate laboratory to study phenomena of the
Standard Model and to test the limits of this theory. To obtain a higher
precision for top quark predictions, the next-to-next-to-leading order (NNLO)
in the pertubative expansion of the top quark production cross-section has to
be calculated. The next-to-leading order (NLO) results are already available
and provide a rather good accuracy. But this precision might be accidental,
because at NLO not all the possible colour exchanges which occur at the
one-loop level are considered and they could have significant impact on the
cross-section and its differential distributions. In order to have precise
predictions of the single top quark production the complete NNLO calculation is
necessary. In this thesis the contributions of the one-loop amplitudes squared
in NNLO are calculated for one production channel ($\textit{t}$-channel). The
other possible production channels of the single top quark are also
investigated. With the presented setup well known results in literature are
reproduced. Intermediate results are calculated with different independent
methods and, if possible, compared with results from literature. The occurring
ultraviolet divergencies are dealt with in conventional dimensional
regularisation (CDR) in the $\bar{\text{MS}}$ scheme ("Modified Minimal
Substraction Scheme"). The final result still has infrared divergencies. An
anti-commuting scheme for the calculation with the $\gamma_5$ matrix in CDR is
used. An alternative scheme for the treatment of $\gamma_5$ is the Larin
scheme, which will be introduced and discussed.
