The quark-gluon plasma is a state of nuclear matter appearing at very high temperature. In the laboratory, it is possible to reach such conditions using heavy-ion collisions at ultra-relativistic energies. The ALICE experiment at LHC is dedicated to the study of the quark-gluon plasma with Pb-Pb collisions at 2.76 TeV. The first part of this study, presented as an annex, will consist in the very first results of the ALICE muon spectrometer, obtained using cosmic rays. The second part will present the evolution of the reconstruction efficiency of the muon spectrometer during its first two years of running. This study will show that the total reconstruction efficiency of the tracking chamber is more than 90% in proton-proton collisions, and 85% in lead-lead collisions. A track selection method based on the value of the product momentum - distance of closest approach will also be presented. This selection will allow to remove the tracks coming from muons produced in collisions between the beam and the residual gas in the beam line, and fake tracks in the most central Pb-Pb collisions. Finally, this thesis will present a first analysis of the production yield of J/psi and single muons as a function of the collision's charged-particle multiplicity in proton-proton collisions.
