Abstract : ALICE, the dedicated heavy ion experiment at the LHC, has also an important physics program with proton-proton collisions. The main purpose of the experiment is to investigate the properties of strongly interacting matter at extreme energy density where the formation of the Quark Gluon Plasma is expected. In this regard, quarkonia and heavy flavours are especially relevant. They will be measured in ALICE through the electron channel and the hadron channel in the central barrel as well as through the muon channel in the forward muon spectrometer. In this contribution, the ALICE muon spectrometer is presented and selected heavy flavour physics topics are reviewed. Special attention is given to the capabilities of the apparatus for the first measurements performed with p-p collisions at √s = 7 TeV