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We report on the studies of Transverse-Momentum-Dependent distributions(TMDs) at a future fixed-target experiment --AFTER@LHC-- using the $p^+$ or Pbion LHC beams, which would be the most energetic fixed-target experiment everperformed. AFTER@LHC opens new domains of particle and nuclear physics bycomplementing collider-mode experiments, in particular those of RHIC and theEIC projects. Both with an extracted beam by a bent crystal or with an internalgas target, the luminosity achieved by AFTER@LHC surpasses that of RHIC by upto 3 orders of magnitude. With an unpolarised target, it allows formeasurements of TMDs such as the Boer-Mulders quark distributions and thedistribution of unpolarised and linearly polarised gluons in unpolarisedprotons. Using polarised targets, one can access the quark and gluon SiversTMDs through single transverse-spin asymmetries in Drell-Yan and quarkoniumproduction. In terms of kinematics, the fixed-target mode combined with adetector covering $\eta_{\rm lab} \in [1,5]$ allows one to measure theseasymmetries at large $x^\uparrow$ in the polarised nucleon.

Studies of Transverse-Momentum-Dependent distributions with A Fixed-Target ExpeRiment using the LHC beams (AFTER@LHC)