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The charmonium states provide essential information on the properties of a new state of matter predicted to be formed at extreme energy densities and temperatures, the Quark Gluon Plasma (QGP). ALICE is an experiment at LHC dedicated to the study of the QGP state in heavy ion collisions. The ALICE results on the J/ψ production using the dielectron decay channel in pp collisions at 7 TeV and Pb-Pb collisions at √sNN = 2.76 TeV will be discussed. Due to its excellent vertexing capabilities, ALICE can separate the non-prompt J//ψ component thus allowing for a measurement of the beauty production. beauty production. ALICE is the only experiment that measures the charmonium production at central rapidity (|y| < 0.9) down to pT=0