Radiative corrections to Higgs-boson production in association with top-quark pairs at e+ e- colliders

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%.