  The article presents the conservative dynamics of gravitationally interacting
two-point-mass systems up to the eight order in the inverse power of the
velocity of light, i.e.\ 4th post-Newtonian (4PN) order, and up to quadratic
order in Newton's gravitational constant. Additionally, all logarithmic terms
at the 4PN order are given as well as terms describing the test-mass limit.
With the aid of the Poincar\'e algebra additional terms are obtained. The
dynamics is presented in form of an autonomous Hamiltonian derived within the
formalism of Arnowitt, Deser and Misner. Out of the 57 different terms of the
4PN Hamiltonian in the center-of-mass frame, the coefficients of 45 of them are
derived. Reduction of the obtained results to circular orbits is performed
resulting in the 4PN-accurate formula for energy expressed in terms of angular
frequency in which two coefficients are obtained for the first time.
