  We construct a global B-model for weighted homogeneous polynomials based on
K. Saito's theory of primitive forms. Our main motivation is to give a rigorous
statement of the so called global mirror symmetry conjecture relating
Gromov-Witten invariants and Fan--Jarvis--Ruan--Witten invariants. Furthermore,
our construction allows us to generalize the notion of a quasi-modular form and
holomorphic anomaly equations. Finally, we prove the global mirror symmetry
conjecture for the Fermat polynomials.
