Abstract : ALICE (A Large Ion Collider Experiment) is the LHC detector dedicated to the study of ultra-relativisic heavy ion collisions. The main goal of ALICE is the study of a new phase of the nuclear matter predicted by the Quantum ChromoDynamics theory (QCD) : the Quark-Gluon Plasma (QGP). One of the possible signature is a suppression of quarkonia yields by color screening in the heavy ion collisions, in which the formation of the QGP is expected. The muon spectrometer will be measured the quarkonia yields (J/Psi, Upsilon) in heavy ion collisions via their dimuon decay. A fast trigger, associated to muon spectrometer, has to select events with at least one muon or one dimuon by using a track search algorithm. The study of muon trigger performances will be presented with emphasis on the trigger efficiency and rates in Ar-Ar and Pb-Pb collisions. We will also present the reconstruction of unlike-sign dimuon mass spectrum with the ALICE muon spectrometer. The expected yields of Upsilon states will be extracted from a simulation based on a fit of this spectrum for one month running for Pb-Pb collisions and for different collision centralities.