  In the paper the possible approaches to the rigorous derivation of the
Boltzmann kinetic equation with hard sphere collisions from underlying dynamics
are considered. In particular, a formalism for the description of the evolution
of infinitely many hard spheres within the framework of marginal observables in
the Boltzmann--Grad scaling limit is developed. Also we give consideration to
one more approach of the description of the kinetic evolution of hard spheres
in terms of a one-particle distribution function governed by the non-Markovian
generalization of the Enskog equation and the Boltzmann--Grad asymptotic
behavior of its non-perturbative solution is established.
