  We construct from a real affine manifold with singularities (a tropical
manifold) a degeneration of Calabi-Yau manifolds. This solves a fundamental
problem in mirror symmetry. Furthermore, a striking feature of our approach is
that it yields an explicit and canonical order-by-order description of the
degeneration via families of tropical trees.
  This gives complete control of the B-model side of mirror symmetry in terms
of tropical geometry. For example, we expect our deformation parameter is a
canonical coordinate, and expect period calculations to be expressible in terms
of tropical curves. We anticipate this will lead to a proof of mirror symmetry
via tropical methods.
  This paper is the key step of the program we initiated in math.AG/0309070.
