[en] We have calculated the single-inclusive production cross section of massive quarks in electron-positron-annihilation with next-to-leading order QCD corrections. With these results we have extracted fragmentation functions for the fragmentation from partons into D⁰, D⁺ and D^* mesons, where we have used experimental data from the B factories Belle and CLEO and from the ALEPH and OPAL experiments at the LEP collider. In our analysis we have included the masses of c and b quarks and of the D mesons and tested the evolution of fragmentation functions with a global fit spanning the B factories' center-of-mass energy of √(s)=10.5 GeV to LEP's run at the Z boson resonance at M_Z. We have applied this fragmentation functions in deep inelastic scattering for comparisons with HERA data using parton cross sections from the literature available in program form. We have then modified this cross section to calculate predictions for deep inelastic two-photon-scattering. By applying the Weizsaecker-Williams spectrum on the real photon we have calculated predictions for LEP1, LEP2 and the future ILC experiments. For ILC we have also included a beamstrahlung spectrum. Finally we have calculated production cross sections for the planned eγ mode of the ILC with the help of a Compton spectrum. (orig.)