  We have calculated the complete O(alpha) and O(alpha_s) radiative corrections
to the Higgs-production process e+ e- -> t anti-t H in the Standard Model. This
process is particularly interesting for the measurement of the top-quark Yukawa
coupling at a future e+ e- collider. The calculation of the O(alpha)
corrections is described in some detail including, in particular, the treatment
of the soft and collinear singularities. The discussion of numerical results
focuses on the total cross section as well as on angular and energy
distributions of the outgoing particles. The electroweak corrections turn out
to be sizable and can reach the order of +/-10%. They result from cancellations
between electromagnetic, fermionic, and weak bosonic corrections, each of which
are of the order of +/-10%.
