  This thesis explores an exotic class of M-theory compactifications in which
the compact manifold is taken to be a Calabi-Yau five-fold. The resulting
effective theory is a one-dimensional N=2 super-mechanics model that exhibits
peculiar features of one-dimensional supersymmetry, such as the appearance of
fermion-only super-multiplets. The latter necessitates reducing also the
fermionic sector of M-theory, which is not normally included in the
compactification literature and is thus presented, together with the required
technology, in detail. The one-dimensional effective theory is most elegantly
described in superspace and therefore, a detailed account of one-dimensional
flat and curved N=2 superspace is provided. This includes developing the theory
of fermionic multiplets and the study of cross-couplings between 2a and 2b
multiplets. Another important aspect is the inclusion of flux. We study its
consistency conditions, its relation to supersymmetry and the way it gives rise
to a potential in the one-dimensional effective action. It is also explained
how the supersymmetry-preserving part of the potential can be obtained from a
Gukov-type superpotential. The main motivation of this compactification
scenario is rooted in the realm of cosmology. Its virtue is a democratic
treatment of spatial dimensions. As opposed to the artificial 3+7 split in most
string compactifications, the early universe starts out with all spatial
dimensions compact and small in our approach. One then seeks for dynamical ways
in which three dimensions grow large at late times. Possible realisations of
this idea are discussed both at the classical and at the quantum level.
Finally, preliminary work on Calabi-Yau five-fold compactifications of F-theory
and the resulting two-dimensional string-like actions is presented.
