  This is the author's Habilitation which took place at University of Essen on
July 11, 1993. The manuscript contains two parts. The first one is devoted to
the author's combinatorial construction of mirrors of Calabi-Yau hypersurfaces
in Gorenstein toric Fano varieties. The second one contains author's results on
the variation of mixed Hodge structures of affine hypersurfaces in algebraic
tori and their connection to Gelfand-Kapranov-Zelevinsky theory of generalized
hypergeometric functions and their applications to the mirror symmetry for
Calabi-Yau hypersurfaces in toric varieties.
