Prospective for A Fixed-Target ExpeRiment at the LHC: AFTER @ LHC

We argue that the concept of a multi-purpose fixed-target experiment with the proton or lead-ion LHC beams extracted by a bent crystal would offer a number of ground-breaking precision-physics opportunities. The multi-TeV LHC beams will allow for the most energetic fixed-target experiments ever performed. The fixed-target mode has the advantage of allowing for high luminosities, spin measurements with a polarised target, and access over the full backward rapidity domain --uncharted until now-- up to x_F ~ -1.