Spin physics with a fixed-target experiment at the LHC

The multi-TeV proton and ion beams of the LHC would allow for the most energetic fixed-target experiment ever. In particular, pp, pd and pA collisions could be performed at √sNN = 115 GeV, as well as Pbp and PbA collisions at √sNN = 72 GeV, in a parasitic way by making use of the already existing LHCb and ALICE detectors in fixed-target mode. This would offer the possibility to carry out a ground-breaking physics program, to study the nucleon and nuclear structure at high x, the spin content of the nucleon and the phases of the nuclear matter from a new rapidity viewpoint. In this talk I focus on the spin physics axis of the full program developed so far by the AFTER@LHC study group.