We associate to any convenient nondegenerate Laurent polynomial $f$ on the complex torus ${\left({ℂ}^{*}\right)}^n$ a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of $f$ (or its universal unfolding) and of the corresponding Hodge theory.