  We construct compact examples of D-manifolds for type IIB strings. The
construction has a natural interpretation in terms of compactification of a 12
dimensional `F-theory'. We provide evidence for a more natural reformulation of
type IIB theory in terms of F-theory. Compactification of M-theory on a
manifold $K$ which admits elliptic fibration is equivalent to compactification
of F-theory on $K\times S^1$. A large class of $N=1$ theories in 6 dimensions
are obtained by compactification of F-theory on Calabi-Yau threefolds. A class
of phenomenologically promising compactifications of F-theory is on $Spin(7)$
holonomy manifolds down to 4 dimensions. This may provide a concrete
realization of Witten's proposal for solving the cosmological constant problem
in four dimensions.
