  We study kaonic deuterium, the bound K^-d state A_(K d). Within a quantum
field theoretic and relativistic covariant approach we derive the energy level
displacement of the ground state of kaonic deuterium in terms of the amplitude
of K^-d scattering for arbitrary relative momenta. Near threshold our formula
reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering
near threshold is defined by the resonances Lambda(1405), Sigma(1750) and a
smooth elastic background, and the inelastic channels K^- d -> NY and K^- d ->
NY pion, with Y = Sigma^(+/-), Sigma^0 and Lambda^0, where the final-state
interactions play an important role. The Ericson-Weise formula for the S-wave
scattering length of K^-d scattering is derived. The total width of the energy
level of the ground state of kaonic deuterium is estimated using the
theoretical predictions of the partial widths of the two-body decays A_(Kd) ->
NY and experimental data on the rates of the NY-pair production in the
reactions K^-d -> NY. We obtain Gamma_{1s} = (630 +/-100) eV. For the shift of
the energy level of the ground state of kaonic deuterium we predict
epsilon_(1s) = (353 +/-60)eV.
