Quarkonia states are expected to provide essential information on the properties of the high-density strongly-interacting system formed in the early stages of high-energy heavy-ion collisions. ALICE is the LHC experiment dedicated to the study of nucleus-nucleus collisions and can study charmonia at forward rapidity (2.5 < y < 4) via the mu+ mu- decay channel and at mid rapidity (|y| < 0.9) via the e+ e- decay channel. In both cases charmonia are measured down to zero transverse momentum. The inclusive J/psi production as a function of transverse momentum and rapidity in pp collisions at sqrt{s} = 2.76 and 7 TeV are presented. For pp collisions at sqrt{s} = 7 TeV, the inclusive J/psi production as a function of the charged particle multiplicity, the inclusive J/psi polarization at forward rapidity and the J/psi prompt to non-prompt fraction are discussed. Finally, the analysis of the inclusive J/psi production in the Pb-Pb data collected fall 2011 at a center of mass energy of sqrt{s_{NN}} = 2.76 TeV is presented. Results on the nuclear modification factor are then shown as a function of centrality, transverse momentum and rapidity and compared to model predictions. First results on inclusive J/psi elliptic flow are given.
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