Higgs production in $e$ and real $gamma$ collision

We investigate the Standard Model Higgs boson production in $e^-gamma$ collision. The electroweak one-loop contributions to the scattering amplitude for $e^-gammarightarrow e^-H$ are calculated and expressed in analytical form. We analyze the cross section for the Higgs production in $e^-gamma$ collision for each combination of polarizations of the initial electron and photon beams. The feasibility of observing the Higgs boson in $e^-+gammarightarrow e^-+b+{overline b}$ channel is examined.