Quarkonium production measurements with the ALICE detector at the LHC

In this new energy regime, quarkonium provides a unique probe to study the properties of the high-density, strongly interacting system formed in the early stages of high-energy heavy-ion collisions. In ALICE, quarkonium states are reconstructed down to p_T=0 via their mu+mu- decay channel in the muon spectrometer (2.5<y<4.0) and via their e+e- channel in the central barrel (|y|<0.9). Measurement of the transverse momentum and rapidity distributions of inclusive J/psi production cross section in proton-proton collisions at sqrt{s}=2.76 and 7 TeV will be presented. We will discuss the dependence on charged particle multiplicity of the inclusive J/psi yield in proton-proton collisions at sqrt{s}=7 TeV. Finally, the analysis of the inclusive J/psi production in Pb-Pb collisions at sqrt{s_NN}=2.76 TeV will be described. Preliminary results on the nuclear modification factor (R_AA) and the central to peripheral nuclear modification factor (R_CP) will be discussed.