  We consider gauge theories defined in higher dimensions where the extra
dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these
gauge theories as four-dimensional theories with Kaluza-Klein modes. We then
perform a generalized `a la Forgacs-Manton dimensional reduction. We emphasize
some striking features emerging such as (i) the appearance of non-abelian gauge
theories in four dimensions starting from an abelian gauge theory in higher
dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory
takes place entirely in the extra dimensions and (iii) the renormalizability of
the theory both in higher as well as in four dimensions.
