The ALICE experiment is the LHC detector mainly dedicated to the study of the Quark Gluon Plasma (QGP) in Pb-Pb collisions. The detector has started the data taking less than one year ago, delivering immediately relevant results. An overview of the first physics results obtained in the first six month of running of the experiment will be summarized, giving special emphasis to heavy flavour measurements. Heavy flavours are ideal probes to explore both the formation and properties of the QGP, since they experience the full collision history and are expected to be copiously produced at LHC, much more than at any other collider. With ALICE we will measure heavy flavours down to small transverse momentum, combining hadronic and leptonic channels, both at central and forward rapidity. In particular, in the central rapidity region, it is possible to exclusively reconstruct open charm mesons and baryons via hadronic decay channels. Furthermore, the good identification of electrons allows to measure the production both of charmonium and open beauty. First results from p-p collisions at 7 TeV will be shown, including the clear signals of open and hidden charm hadrons reconstructed at ALICE. These data provide interesting insight into QCD processes in a new energy regime, are important as a baseline for the Pb-Pb program and demonstrate the potential for heavy flavour cross section measurements with the ALICE detector.