  It is believed that strong ferromagnetic orders in some solids are generated
by subtle interplay between quantum many-body effects and spin-independent
Coulomb interactions between electrons. Here we describe our rigorous and
constructive approach to ferromagnetism in the Hubbard model, which is a
standard idealized model for strongly interacting electrons in a solid. We
introduce a class of Hubbard models in any dimensions which are nonsingular in
the sense that both the Coulomb interaction and the density of states (at the
Fermi level) are finite. We then prove that the ground states of the models
exhibit saturated ferromagnetism, i.e., have maximum total spins. Combined with
our earlier results, the present work provides nonsingular models of itinerant
electrons with only spin-independent interactions where low energy behaviors
are proved to be that of a ``healthy'' ferromagnetic insulator.
