Beam extraction technique by a bent crystal offers the possibility to
obtain a clean and collimated high energy beam without altering the
performance of the LHC. The multi-TeV proton and ion beams will allow
for the most energetic fixed-target experiments ever performed with
high luminosities. Such an experiment, tentatively named AFTER for "A
Fixed Target ExpeRiment" gives access to new domains of particle and
nuclear physics complementing that of collider experiments, in
particular, that of the Brookhaven's Relativistic Heavy Ion Collider
(RHIC) and the projects of Electron-ion colliders (EIC). By
instrumenting the target-rapidity region, gluon and heavy-quark
distributions in the proton, the neutron and the nuclei can be
accessed at large x. The fixed-target mode has the advantage to allow
for spin measurements with polarized target and for target-species
versatility providing the opportunity to study nuclear matter,
including the quark-gluon plasma. In this seminar, I will outline the
physics opportunities offered by the fixed-target mode at the LHC as
well as the expected luminosities and I will present a tentative
design for the AFTER experiment.