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In this report we discuss the organization of different levels of nature andthe corresponding space-time structures by the consideration of a particularproblem of time irreversibility. The fundamental time irreversibility problemconsists in the following: how to reconcile the time-reversible microscopicdynamics and the irreversible macroscopic one. The recently proposed functionalformulation of mechanics is aimed to solve this problem. The basic concept ofthis formulation is not a material point and a trajectory, like in thetraditional formulation of mechanics, but a probability density function. Evenif we deal with a single particle (not with an ensemble of particles), wedescribe its state as a probability density function. We justify this approachusing measurement theory. A particular problem in the framework of theirreversibility problem is the derivation of the Boltzmann kinetic equationfrom the equations of microscopic dynamics. We propose a procedure forobtaining the Boltzmann equation from the Liouville equation based on the BBGKYhierarchy, the recently proposed functional formulation of classical mechanics,and the distinguishing between two scales of space-time, i.e., macro- andmicroscale. The notion of a space-time structure is introduced. It takes intoaccount not only the space-time itself (i.e., a pseudo-Riemannian manifold),but also a characteristic length and time. The space-time structures form ahierarchy in sense that the initial values for the processes on the microscopicspace-time structure (interactions of the particles) are assigned from theprocesses on the macroscopic one (kinetic phenomena).

Hierarchy of space-time structures, Boltzmann equation, and functional mechanics