D^*\mu coincidences are studied using data taken with the H1 detector at HERA during the years 1997 to 2000, corresponding to an integrated luminosity of about 90 pb^-1. With the aid of charge and angle correlations between the D^* and the muon, a separation of charm and beauty production contributions is possible. Total charm and beauty production cross sections are shown as well as differential cross sections of several D^*\mu quantities and compared with the prediction of Leading Order (LO) Monte Carlo calculations. In a separate analysis inclusive charm production is studied using e⁺p data taken with the H1 detector during the years 1999 to 2000, corresponding to an integrated luminosity of about 48 pb^-1. For the charmed mesons D^*, D⁰, D_s and D⁺ total production cross sections are determined and differential distributions are measured for the D⁺ and D⁰ mesons, whereby lifetime information is used to improve the signal qualities. The results are compared with predictions, based on LO Monte Carlo simulations. The measured production cross sections are used to determine fragmentation ratios, which are then compared with values measured e.g. at e⁺ e^- colliders.

PACS numbers: 13.60.Le, 14.65.Dw, 14.65.Fy