A theoretical analysis of the collisions of particles with deuterons is carried out in the high-energy approximation. This approximation, which corresponds to a generalized form of diffraction theory, takes explicit account of double collision processes as well as single ones. It is used to express the amplitudes for elastic and inelastic scattering by deuterons in terms of the elastic-scattering amplitudes of the neutron and proton and the deuteron wave functions. The resulting expressions are used to evaluate the differential cross section for elastic scattering, and the angular distribution of inelastic scattering (i.e., the differential cross section for deuteron breakup integrated over final energies of the incident particle). The contributions to these cross sections of the various single and double scattering processes and the terms which represent their interference are exhibited individually. Expressions are derived for the total cross section of the deuteron and for its elastic and inelastic total scattering and absorption cross sections. The difference between the various types of deuteron cross sections and the sum of the corresponding cross sections for the free neutron and proton is explained in some detail. Spin-dependent interactions are treated, and for incident particles of spin 1/2 an expression is given for the deuteron total cross section in terms of the general spin-dependent scattering amplitudes of the neutron and proton. The theory is applied to antiproton-deuteron collisions in the energy range from 0.13 to 17.1 BeV. The results for the total and absorption cross sections which are calculated for a variety of models of the deuteron wave function are found to be in good agreement with the measurements. The magnitudes of such effects as double scattering and the interference of single-and double-scattering amplitudes are seen to be appreciable.