Several measurements of single top quark production in proton-proton collisions at the LHC at centre-of-mass energies of 7, 8 and 13 TeV, using data collected with the CMS experiment, are presented. The analyses investigate separately the productions of top via t-channel exchange, in association with a W boson (tW) or via the s-channel. Final states with at least one charged lepton and one b-jet are explored to measure inclusive production cross sections. Fiducial and differential cross section measurements in the t-channel are also reported. The measurements can be used to constrain directly the Vtb CKM matrix element by comparing with the most precise standard model theory predictions. Measurements of rare processes involving a top quark and a neutral EWK boson (Z or photon) are also discussed.