  A detailed account is given on approximation schemes to the Einstein theory
of general relativity where the iteration starts from the Newton theory of
gravity. Two different coordinate conditions are used to represent the Einstein
field equations, the generalized isotropic ones of the canonical formalism of
Arnowitt, Deser, and Misner and the harmonic ones of the Lorentz-covariant
Fock-de Donder approach. Conserved quantities of isolated systems are
identified and the Poincar\'e algebra is introduced. Post-Newtonian expansions
are performed in the near and far (radiation) zones. The natural fitting of
multipole expansions to post-Newtonian schemes is emphasized. The treated
matter models are ideal fluids, pure point masses, and point masses with spin
and mass-quadrupole moments modelling rotating black holes. Various
Hamiltonians of spinning binaries are presented in explicit forms to higher
post-Newtonian orders. The delicate use of black holes in post-Newtonian
expansion calculations and of the Dirac delta function in general relativity
find discussions.
