  We study string compactifications with sixteen supersymmetries. The moduli
space for these compactifications becomes quite intricate in lower dimensions,
partly because there are many different irreducible components. We focus
primarily, but not exclusively, on compactifications to seven or more
dimensions. These vacua can be realized in a number ways: the perturbative
constructions we study include toroidal compactifications of the heterotic/type
I strings, asymmetric orbifolds, and orientifolds. In addition, we describe
less conventional M and F theory compactifications on smooth spaces. The last
class of vacua considered are compactifications on singular spaces with
non-trivial discrete fluxes.
  We find a number of new components in the string moduli space. Contained in
some of these components are M theory compactifications with novel kinds of
``frozen'' singularities. We are naturally led to conjecture the existence of
new dualities relating spaces with different singular geometries and fluxes. As
our study of these vacua unfolds, we also learn about additional topics
including: F theory on spaces without section, automorphisms of del Pezzo
surfaces, and novel physics (and puzzles) from equivariant K-theory. Lastly, we
comment on how the data we gain about the M theory three-form might be
interpreted.
