  We show the construction of the dual superconducting theory for the
confinement mechanism from QCD in the maximally abelian (MA) gauge using the
lattice QCD Monte Carlo simulation. We find that essence of infrared abelian
dominance is naturally understood with the off-diagonal gluon mass $m_{\rm off}
\simeq 1.2 {\rm GeV}$ induced by the MA gauge fixing. In the MA gauge, the
off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon
phase tends to be random. As the mathematical origin of abelian dominance for
confinement, we demonstrate that the strong randomness of the off-diagonal
gluon phase leads to abelian dominance for the string tension. In the MA gauge,
there appears the macroscopic network of the monopole world-line covering the
whole system. We investigate the monopole-current system in the MA gauge by
analyzing the dual gluon field $B_\mu$. We evaluate the dual gluon mass as $m_B
= 0.4 \sim$ 0.5GeV in the infrared region, which is the lattice-QCD evidence of
the dual Higgs mechanism by monopole condensation. Owing to infrared abelian
dominance and infrared monopole condensation, QCD in the MA gauge is
describable with the dual Ginzburg-Landau theory.
