  We present some mathematical aspects of Landau-Ginzburg string vacua in terms
of toric geometry. The one-to-one correspondence between toric divisors and
some of (-1,1) states in Landau-Ginzburg model is presented for superpotentials
of typical types. The Landau-Ginzburg interpretation of non-toric divisors is
also presented. Using this interpretation, we propose a method to solve the
so-called "twisted sector problem" by orbifold construction. Moreover,this
construction shows that the moduli spaces of the original Landau-Ginzburg
string vacua and their orbifolds are connected. By considering the mirror map
of Landau-Ginzburg models, we obtain the relation between Mori vectors and the
twist operators of our orbifoldization. This consideration enables us to argue
the embedding of the Seiberg-Witten curve in the defining equation of the
Calabi-Yau manifoulds on which the type II string gets compactified. Related
topics concerning the Calabi-Yau fourfolds and the extremal transition are
discussed.
