[en] The author studies the Dirac operator with a many-center Coulomb potential with regard to the following questions: Self-adjointness, existence of a distinguished self-adjoint extension, stability of eigenvalues. In particular, it is proved that also for many-center Coulomb potentials one can define a distinguished self-adjoint extension by means of a cut-off procedure. In the case of two centers the author studies convergence of the operator as the distance between the centers shrinks to zero. (Auth.)