  Keeping nickel, cobalt and iron in mind, we investigate the origin of the
itinerant ferromagnetism. In so doing, we generalize the Gutzwiller
approximation. In that,we take account of the effect of the band degeneracy and
the Hund's-rule coupling in addition to the on-site repulsion. After the
discussion on nickel, the condition for the incomplete ferromagnetism, observed
in cobalt and iron, is argued. Phase diagrams, which show the interplay between
the band shape peculiarity and the Hund's-rule coupling, are given. It is found
that for the $3d$-transition metal systems, both of the Hund's-rule coupling
and the special feature of the density of states are necessary to explain the
itinerant ferromagnetism.
