J/ψ production in pp collisions and in Pb-Pb collisions at the LHC with the ALICE experiment

We report the recent measurements of the inclusive J/psi production in pp collisions at root s = 2.76 TeV, in pp collisions at root s = 7 TeV and in Pb-Pb collisions at root s(NN) = 2.76 TeV with the ALICE detector at the LHC. The J/psi mesons are detected down to p(T) = 0 GeV/c via their di-muon decay channel at forward rapidity (2.5 < y < 4) and via their di-electron decay channel at mid-rapidity (vertical bar y vertical bar < 0.9). A special emphasis is put on the nuclear modification factor which is compared to the predictions of current J/psi production models.