  The dynamics of an infinite system of point particles in $\mathbb{R}^d$,
which hop and interact with each other, is described at both micro- and
mesoscopic levels. The states of the system are probability measures on the
space of configurations of particles. For a bounded time interval $[0,T)$, the
evolution of states $\mu_0 \mapsto \mu_t$ is shown to hold in a space of
sub-Poissonian measures. This result is obtained by: (a) solving equations for
correlation functions, which yields the evolution $k_0 \mapsto k_t$, $t\in
[0,T)$, in a scale of Banach spaces; (b) proving that each $k_t$ is a
correlation function for a unique measure $\mu_t$. The mesoscopic theory is
based on a Vlasov-type scaling, that yields a mean-field-like approximate
description in terms of the particles' density which obeys a kinetic equation.
The latter equation is rigorously derived from that for the correlation
functions by the scaling procedure. We prove that the kinetic equation has a
unique solution $\varrho_t$, $t\in [0,+\infty)$.
