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 production of top quark 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. Differential cross section measurements in the t-channel are also reported. The measurements can be used to constrain directly the $|V_{tb}|$ CKM matrix element by comparing with the most precise standard model theory predictions. Measurement of a rare process involving a top quark and a Z boson is also discussed.