  We provide a short historic of the early development of kinetic theory in
plasma physics and synthesize the basic kinetic equations describing the
evolution of systems with long-range interactions derived in Paper I. We
describe the evolution of the system as a whole and the relaxation of a test
particle in a bath at equilibrium or out-of-equilibrium. We write these
equations for an arbitrary long-range potential of interaction in a space of
arbitrary dimension d. We discuss the scaling of the relaxation time with the
number of particles for non-singular potentials. For always spatially
homogeneous systems, the relaxation time of the system as a whole scales like N
in d>1 and like N^2 (presumably) in d=1. For always spatially inhomogeneous
systems, the relaxation time of the system as a whole scales like N in any
dimension of space. For one dimensional systems undergoing a dynamical phase
transition from a homogeneous to an inhomogeneous phase, we expect a relaxation
time of the form N^{\delta} with 1<\delta<2 intermediate between the two
previous cases. The relaxation time of a test particle in a bath always scales
like N. We also briefly discuss the kinetic theory of systems with long-range
interactions submitted to an external stochastic potential. This paper gathers
basic equations that are applied to specific systems in Paper III.
