  The Hamiltonian for a system of relativistic bodies interacting by their
gravitational field is found in the post-Minkowskian approximation, including
all terms linear in the gravitational constant. It is given in a surprisingly
simple closed form as a function of canonical variables describing the bodies
only. The field is eliminated by solving inhomogeneous wave equations, applying
transverse-traceless projections, and using the Routh functional. By including
all special relativistic effects our Hamiltonian extends the results described
in classical textbooks of theoretical physics. As an application, the
scattering of relativistic objects is considered.
