  We introduce an integrable time-discretized version of the classical
Calogero-Moser model, which goes to the original model in a continuum limit.
This discrete model is obtained from pole solutions of a semi-discretized
version of the Kadomtsev-Petviashvili equation, leading to a finite-dimensional
symplectic mapping. Lax pair, symplectic structure and sufficient set of
invariants of the discrete Calogero-Moser model are constructed for both the
rational and elliptic cases. The classical $r$-matrix is the same as for the
continuum model. An exact solution of the initial value problem is given for
the rational discrete-time Calogero-Moser model. The pole-expansion and
elliptic solutions of the fully discretized Kadomtsev-Petviashvili equation are
also discussed.
