Quarkonium production at LHCb

Despite the large experimental and theoretical efforts, the quarkonium production rates and states in hadronic collisions are not yet satisfactorily understood. Strong of its forward geometry, LHCb has the unique opportunity to explore the field of quarkonium production at high rapidity, thus exploring a new and unknown territory. We report the measurement of the double differential $J/\psi$, $\psi (2S)$ and $\Upsilon$ cross section at LHCb with the data sample recorded by the LHCb experiment during the 2010 data taking. The $J/\psi$ and $\psi(2S)$ prompt components are separated from the products of $b$-hadrons decays using topological information. The results will be compared with several theoretical models and other experiments. Preliminary results and prospects for the other quarkonium states and the polarisation will also be given.