  We study monopoles and gluon fields in QCD in the maximally abelian (MA)
gauge in the context of the dual superconductor picture for confinement. In the
abelian gauge, unit-charge magnetic monopoles appear, but multi-charge
monopoles do not in general cases. The appearance of the monopole is studied
using the gauge-connection formalism in relation to the SU($N_c$) singular
gauge transformation. The relevant role of off-diagonal gluons is found for the
appearance of monopoles in the abelian gauge in QCD. We study the gluon-field
properties around the monopole in the MA gauge in terms of the action density
using the lattice QCD. The monopole provides infinitely large field
fluctuations in the abelian sector. In the MA gauge, off-diagonal gluons are
strongly suppressed but largely remain around the monopole, which indicates the
effective size and the structure of monopoles. We find the large cancellation
between the abelian part and the off-diagonal part of the action density around
the monopole in the MA gauge. Owing to this cancellation, the monopole can
appear in QCD without large cost of the QCD action. Finally, we generalize the
framework of the abelian projection, {\it i.e.} the extraction of the abelian
gauge manifold from QCD, by introducing the `gluonic Higgs field' $\vec
\phi_D[A_\mu(x)]$ defined from the ${\rm SU}(N_c)$ covariant derivative $\hat
D_\mu$. By way of $\vec \phi_D[A_\mu(x)]$, the maximally abelian projection can
be performed in the gauge-covariant manner without the notion of gauge fixing
in principle.
