The ALICE forward muon spectrometer studies the complete spectrum of heavy quarkonia (J/Ψ, Ψ′, ϒ, ϒ′, ϒ′′) via their decay in the μ+μ– channel. Heavy quarkonium states, provide an essential tool to study the early and hot stage of heavy-ion collisions. In particular they are expected to be sensitive to Quark-Gluon Plasma formation. In the presence of a deconfined medium (i.e. QGP) with high enough energy density, quarkonium states are dissociated because of colour screening. This leads to a suppression of their production rates. At the high LHC collision energy, both the charmonium states (J/Ψ and Ψ′) as well as the bottomonium states (ϒ, ϒ′ and ϒ′′) can be studied. The Dimuon spectrometer is optimized for the detection of these heavy quark resonances.