Charmonium production is a key observable in the study of the properties of the Quark-Gluon Plasma created in ultrarelativistic heavy-ion collisions. The ALICE detector at the LHC provides unique capabilities at mid-rapidity to study charmonium production at low transverse momentum. J/psi mesons can be reconstructed via their dielectron decay channel. This thesis presents the measurement of inclusive J/psi production in Pb-Pb collisions at the center of mass energy of sqrt(s_NN)= 5.02 TeV. Due to the large integrated luminosity collected by ALICE during the second stage of operation of the LHC, the inclusive J/psi nuclear modification factor was measured as a function of centrality and as a function of transverse momentum in different centrality classes. The inclusive J/psi nuclear modification factor exhibits an enhancement towards lower transverse momentum, reaching a value around unity, and a suppression at high transverse momentum where energy-loss mechanisms are dominant. A qualitative description of the measurements is achieved by the models which include a large fraction of J/psi production by recombination. In addition, in peripheral collisions, the observation at mid-rapidity of an excess of J/psi with low transverse momentum (< 150 MeV/c) is presented
