  We present the basic non-perturbative structure of the space of classical
dynamical solutions and corresponding one particle quantum states in SU(3)
Yang-Mills theory. It has been demonstrated that the Weyl group of su(3)
algebra plays an important role in constructing non-perturbative solutions and
leads to profound changes in the structure of the classical and quantum
Yang-Mills theory. We show that the Weyl group as a non-trivial color subgroup
of SU(3) admits singlet irreducible representations on a space of classical
dynamical solutions which lead to strict concepts of one particle quantum
states for gluons and quarks. The Yang-Mills theory is a non-linear theory and,
in general, it is not possible to construct a Hilbert space of classical
solutions and quantum states as a linear vector space, so, usually, a
perturbative approach is applied. We propose a non-perturbative approach based
on Weyl symmetric solutions to full non-linear equations of motion and
construct a full space of dynamical solutions representing an infinite but
countable solution space classified by a finite set of integer numbers. It has
been proved that the Weyl singlet structure of classical solutions provides the
existence of a stable non-degenerate vacuum which serves as a main precondition
of the color confinement phenomenon. Some physical implications in quantum
chromodynamics are considered.
