  I present a calculation of soft-gluon corrections to single top quark
production in pp collisions at the LHC via the Standard Model partonic
processes in the t and s channels and associated top quark and W boson
production. Higher-order soft-gluon corrections through
next-to-next-to-next-to-leading order (NNNLO) are calculated at next-to-leading
logarithmic (NLL) accuracy. The soft-gluon corrections in the s channel and in
tW production are large and dominant, while in the t channel they are not a
good approximation of the complete QCD corrections.
