  We review the major mathematical concepts involved in the dimensional
reduction of D=11 N=1 supergravity theory over a Calabi-Yau manifold with
non-trivial complex structure moduli resulting in ungauged D=5 N=2 supergravity
theory with hypermultiplets. This last has a particularly rich structure with
many underlying geometries. We reproduce the entire calculation and
particularly emphasize its symplectic symmetry and how that arises from the
topology of the underlying subspace. The review is intended to fill in a
specific gap in the literature with the hope that it would be useful to both
the beginner and the expert alike.
