Quarkonia are meson states whose constituents are a charm or bottom quark and its correspondingantiquark (Q¯Q). The study of the production of such bound states in high-energy hadron collisionsrepresents an important test for the Quantum Chromo-Dynamics. Despite the fact that the quarkoniumsaga has already a 40-year history, the quarkonium production mechanism is still an open issue.Therefore, measurements at the new CERN Large Hadron Collider (LHC) energy regimes are extremelyinteresting.In this thesis, the study of inclusive J/ψ production in proton-proton (pp) collisions at √s = 2.76and 7 TeV, obtained with the ALICE experiment, is presented. J/ψ mesons are measured at forwardrapidity (2.5 < y < 4), down to zero pT, via their decay into muon pairs (μ+μ−).Quarkonium resonances also play an important role in probing the properties of the stronglyinteracting hadronic matter created, at high energy densities, in heavy-ion collisions. Under suchextreme conditions, the created system, according to QCD, undergoes a phase transition from ordinaryhadronic matter to a new state of deconfined quarks and gluons, called Quark Gluon Plasma(QGP). The ALICE experiment at CERN LHC has been specifically designed to study this state ofmatter. Quarkonia, among other probes, represents one of the most promising tools to prove the QGPformation. In order to correctly interpret the measurements of quarkonium production in heavy-ioncollisions, a solid baseline is provided by the analogous results obtained in pp collisions.Hence, the work discussed in this thesis, concerning the inclusive J/ψ production in pp collisions,also provides the necessary reference for the corresponding measurements performed in Pb-Pb collisionswhich were collected, by the ALICE experiment, at the very same center-of-mass energy pernucleon pair (√sNN = 2.76 TeV).
