  In this report we discuss the organization of different levels of nature and
the corresponding space-time structures by the consideration of a particular
problem of time irreversibility. The fundamental time irreversibility problem
consists in the following: how to reconcile the time-reversible microscopic
dynamics and the irreversible macroscopic one. The recently proposed functional
formulation of mechanics is aimed to solve this problem. The basic concept of
this formulation is not a material point and a trajectory, like in the
traditional formulation of mechanics, but a probability density function. Even
if we deal with a single particle (not with an ensemble of particles), we
describe its state as a probability density function. We justify this approach
using measurement theory. A particular problem in the framework of the
irreversibility problem is the derivation of the Boltzmann kinetic equation
from the equations of microscopic dynamics. We propose a procedure for
obtaining the Boltzmann equation from the Liouville equation based on the BBGKY
hierarchy, the recently proposed functional formulation of classical mechanics,
and the distinguishing between two scales of space-time, i.e., macro- and
microscale. The notion of a space-time structure is introduced. It takes into
account not only the space-time itself (i.e., a pseudo-Riemannian manifold),
but also a characteristic length and time. The space-time structures form a
hierarchy in sense that the initial values for the processes on the microscopic
space-time structure (interactions of the particles) are assigned from the
processes on the macroscopic one (kinetic phenomena).
