Quantum Chromodynamics predicts that the hot and dense matter produced in ultra-relativistic heavy-ion collisions, the Quark Gluon Plasma (QGP), behaves as a deconfined state of quarks and gluons. Since 1980's it was predicted that quarkonia are suppressed due to screening effects in the QGP, making quarkonia a good tool to probe the plasma.ALICE is the only experiment at the LHC that was designed and built to characterize the physics of the QGP. The muon spectrometer, one of the detectors in ALICE, is used to measure the quarkonia production at forward rapidity. In this thesis the efficiency of the tracking chambers of the muon spectrometer is studied along one year of data taking. The results obtained from real data are compared to simulations in order to compute the systematic uncertainties associated to the tracking apparatus.A complete analysis of the inclusive J/psi --> mu^+ mu^- production in the 2011 Pb-Pb collisions is also presented. The study includes the signal extraction, normalization and acceptance times efficiency corrections. An important part is dedicated to the quantify the systematic uncertainties arising from different sources. The resulting R_{AA} and p_{T} are compared to previous experiments and also to theoretical models.