[en] This thesis presents a measurement of double-tagged charm quark pair production via the process ep→e' ccX→e' D*μX' in lepton-proton collisions at HERA, using an integrated luminosity of 114 pb^-1 gated by the ZEUS detector in the years 1996-2000. Since the charm quark mass provides a large enough energy scale, the perturbative Quantum Chromo-Dynamics approach can be used to calculate the cross section for charm D*-muon pairs. Using the D*-muon pair to tag the charm quark pair, the measurement is sensitive not only to properties of the leading order hard scattering process but also to the hadronisation and the parton density in the proton as well as higher order effects. Employing the angular and charge correlations between the D* meson and the muon, the fraction of charm events is extracted from the data. Cross sections for charm D*-muon pair production in the visible range of the D* transverse momentum p_T^D*>1.5 GeV, the D* pseudorapidity vertical stroke η^D* vertical stroke <1.5, the muon transverse momentum p_T^μ>1.0 GeV and the muon pseudorapidity vertical stroke η^μ vertical stroke <2.2 are measured for the inclusive, photoproduction (inelasticity 0.05< y<0.8 at Q²<1 GeV²) and deep inelastic scattering (y<0.65 at Q²>2 GeV²) regimes. For the inclusive and photoproduction regimes differential cross sections in various kinematic variables of the D*-muon pair are measured as well. The differential cross sections for the inclusive regime are compared to the leading order plus parton shower MC approach, while the differential cross sections for the photoproduction regime are compared to next-to leading order calculations. The momentum fraction carried by the gluon in the proton is also measured. The possibility of extending the Global Track Trigger of the ZEUS DAQ/trigger system with a forward trigger algorithm is the technical task of this thesis. A forward trigger algorithm has been written which finds the event vertex position using STT and FMVD detector data. (orig.)