  The calculations for the production of heavy quarks in deeply inelastic
scattering (DIS) can be seen as an illustrative example in the framework of
perturbative Quantum Chromo Dynamics (pQCD). In this thesis, I give an overview
of all steps that are required for this computation. First, I give an
introduction to the fundamental theoretical basics. Next, I present the
calculation of the matrix elements which are a main part of the work. The
next-to-leading order (NLO) pQCD corrections for polarized DIS have been
obtained here for the first time. Then, I discuss two different phase space
decompositions which provide another important ingredient to the performed
study. Practical results of the computations are shown first on a partonic
level and, next, I present some phenomenological applications on a hadronic
level. These results shed a first light onto the physical opportunities at a
future Electron-Ion Collider (EIC).
