  In heavy-ion collisions at the LHC, the ALICE Collaboration is studying
Quantum Chromodynamics (QCD) matter at very high energy density where the
formation of a Quark Gluon Plasma (QGP) is expected. Quarkonium production is
an important probe to characterize the QGP properties. High precision data in
pp collisions provide the baseline of Pb-Pb measurements and p-Pb collisions
serve to quantify the amount of initial and/or final state effects, related to
cold nuclear matter, that are largely unknown at the LHC energy. Since 2010,
the LHC provided Pb-Pb collisions at sqrt{s_{NN}} = 2.76 TeV, pp collisions at
various energies and in 2013 p-Pb collisions at sqrt{s_{NN}} = 5.02 TeV. In
ALICE, quarkonia can be reconstructed at forward rapidity in the dimuon channel
and at mid-rapidity in the dielectron channel, and, for both channels, down to
zero transverse momentum. New measurements on inclusive production of J/psi,
psi (2S) and Upsilon performed in p-Pb collisions and on the p_T dependence of
inclusive J/psi in Pb-Pb collisions are presented. The contribution of J/psi
from B hadrons to the inclusive production in Pb-Pb is also discussed. Finally,
an estimation of the cold nuclear matter effect in Pb-Pb, extrapolated from
p-Pb measurements, is given.
