The measurement of the heavy-flavour production cross sections in pp collisions at the LHC will allow to test perturbative QCD calculations in a new energy domain. Moreover, within the physics program of the ALICE experiment, it will provide the reference for the study of medium effects in Pb-Pb collisions, where heavy quarks are regarded as sensitive probes of parton-medium interaction dynamics. We present the status and first preliminary results of charm and beauty production measurements with the ALICE experiment, using hadronic D meson decays and semi-leptonic D and B meson decays, including the first cross section measurement of muons from heavy flavour decays at forward rapidity. We also describe the preliminary cross section measurement for J/psi production, obtained using the di-electron decay channel at central rapidity and the di-muon decay channel at forward rapidity.
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