  We study theoretical bases of the dual Higgs theory for confinement physics
in QCD in terms of monopoles and the gluon configuration in the maximally
abelian (MA) gauge. Abelian dominance for the confinement force can be
analytically proved by regarding the off-diagonal angle variable as a random
variable in the lattice formalism. In the long-distance scale, the contribution
of off-diagonal gluons to the Wilson loop cancels each other and exhibits a
perimeter law behavior, which leads to exact abelian dominance on the string
tension if the finite size effect of the Wilson loop is removed. We investigate
the appearance of the monopole in the QCD vacuum, considering the role of
off-diagonal gluons. The monopole carries a large fluctuation of the gluon
field and provides a large abelian action in abelian projected QCD. Due to the
partial cancellation between the abelian part and the off-diagonal part of the
QCD action, the monopole can appear in QCD without large cost of the QCD
action. The off-diagonal gluon is necessary for existence of the monopole at
the short-distance scale. We study monopole condensation, which is the
requirement of the dual Higgs theory, by comparing the QCD vacuum with the
monopole-current system. We find that ``entropy'' of monopole-current dominates
than its ``energy'', and the monopole seems to be condensed at the infrared
scale in the QCD vacuum.
