The muon spectrometer in the forward region of ALICE features a very thick and complex front absorber and an additional muon filter consisting of an iron wall 1.2 m thick. Muon candidates selected from tracks penetrating these absorbers are measured precisely in a dedicated set of tracking detectors. Pairs of muons are used to collect the spectrum of heavy-quark vector-meson resonances (J/Psi). Their production rates can be analysed as a function of transverse momentum and collision centrality in order to investigate dissociation due to colour screening. The acceptance of the ALICE Muon Spectrometer covers the pseudorapidity interval 2.5 ≤ η ≤ 4 and the resonances can be detected down to zero transverse momentum.