  The thesis is devoted to the problem of colour confinement in the non-Abelian
Yang-Mills theory (gluon part of Quantum Chromodynamics). A generalisation of
the 3-dimensional Fock-Schwinger gauge is proposed where the Gauss law
constraint is exactly solvable. This simplifies the theory in a finite domain
and incorporates the variables at the boundary into the Hamiltonian formalism.
The dependence of the partition function on the boundary value of the
longitudinal component of the electric field is studied and related to the
mechanism of the confinement-deconfinement transition. The free energy density
is calculated for $SU(2)$ and $SU(3)$ gluodynamics in the mean-field
approximation for the collective variables. Analysis of its minima reveals a
phase transition at a certain temperature, below which the mean collective
variables have nonzero values. This can be interpreted as a
confinement-deconfinement phase transition. In the confinement phase the
chromo-electric flux through any element of the boundary is strictly zero. This
means the singletness with respect to the group of the residual gauge
transformations and hence impossibility of observing coloured objects at
spatial infinity (in asymptotic states). It is demonstrated that our
confinement condition satisfies the traditional confinement criteria. The
Wilson loop for $SU(N)$ theory is shown to satisfy the area law. The ratio of
the transition temperature to the square root of the string tension coefficient
is in a qualitative agreement with the result from lattice Monte Carlo
simulations. In the deconfinement phase the global symmetry $Z_{N}$ (centre of
$SU(N)$) is spontaneously broken by the surface terms. The confinement phase is
characterised by unbroken symmetry with all nontrivial minima having the same
depth and transformable by $Z_{N}$ actions.
