  In this thesis we calculate the NLO one-loop virtual contributions to the QCD
DGLAP splitting functions in a form suitable for Monte Carlo simulations. We
use the standard technique based on the factorization properties of mass
singularities in the light-cone axial gauge \cite{EGMPR79,CFP80} but we propose
a modification to this approach by introducing a New Principal Value
prescription \cite{GJKS14} in which we use the PV prescription for
regularization of {\em all} singularities in the light-cone plus components of
the four-momenta. The main advantage of the NPV prescription is that exclusive
splitting functions calculated with its help can be used for construction of
the Monte-Carlo parton showers. The reason for this is that in the NPV
prescription some of the higher order poles in dimensional $\epsilon$ parameter
are replaced by the logarithms of a cut-off parameter $\delta$ which has a
geometrical meaning in four dimensions. As a consequence, cancellation of the
higher order poles between real and virtual components is reduced. On the other
hand, at the inclusive level the NPV results agree with the results in the
standard PV prescription which shows compatibility of both approaches.
  With the help of the NPV prescription, we calculate virtual one-loop
contributions to the NLO non-singlet splitting function $P_{q\to q}^{NLO}$ and
selected contributions to the singlet $P_{g\to g}^{NLO}$ one. We also discuss
the dependence of the results on the choice of the integration variable related
to the evolution time in Monte Carlo parton showers. Finally, we present the
{\tt Axiloop} package written in Wolfram Mathematica language, that is
dedicated to perform NLO calculations in the axial gauge. Results presented in
this thesis were obtained with the help of the {\tt Axiloop} package.
