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 $e^{-}\gamma \to e^{-}H$ 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 $e^{-}+\gamma \to e^{-}+b+\bar{b}$ channel is examined.