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Production of single top quark - results from the Tevatron and the LHC

We present the most recent measurements of single top quark production cross section by the CDF and D0 experiments at the Fermilab Tevatron Collider and the ATLAS and CMS experiments at the Large Hadron Collider (LHC). The data were collected at the Tevatron corresponding to an integrated luminosity of up to 9.7 fb$^{-1}$ of proton-antiproton ($p\bar p$) collisions at a centre-of-mass energy of 1.96 TeV and at the LHC corresponding to an integrated luminosity of up to 4.9 fb$^{-1}$ of proton-proton ($pp$) collisions at a centre-of-mass energy of 7 TeV in 2011 and up to 20.3 fb$^{-1}$ at a centre-of-mass energy of 8 TeV in 2012. The measurements of single top quark production in $s$-channel, $t$-channel and associated production of a top quark and a $W$-boson ($tW$ production) are presented separately and lower limits on the CKM matrix element $|V_{tb}|$ from the single top quark cross section are set.