  We develop the formalism for canonical reduction of $(1+1)$--dimensional
gravity coupled with a set of point particles by eliminating constraints and
imposing coordinate conditions. The formalism itself is quite analogous to the
$(3+1)$--dimensional case; however in $(1+1)$ dimensions an auxiliary scalar
field is shown to have an important role. The reduced Hamiltonian is expressed
as a form of spatial integral of the second derivative of the scalar field.
Since in $(1+1)$ dimensions there exists no dynamical degree of freedom of the
gravitational field ({\it i.e.} the transverse-traceless part of the metric
tensor is zero), the reduced Hamiltonian is completely determined in terms of
the particles' canonical variables (coordinates and momenta). The explicit form
of the Hamiltonian is calculated both in post-linear and post-Newtonian
approximations.
