The notion of a Frobenius manifold was introduced by Dubrovin in 1991 [Du1], motivated by topological field theory. It has been studied since then by him, Manin, Kontsevich, and many others. It plays a role in quantum cohomology [Man2] and in mirror symmetry.

But the first big class of Frobenius manifolds had already been constructed in 1983 in singularity theory. K. Saito [SK6][SK9] studied the semiuniversal unfolding of an isolated hypersurface singularity and its Gauß–Manin connection. He was interested in period maps and defined the primitive forms as volume forms with very special properties in relation to the Gauß–Manin connection.

Any primitive form provides the base space of a semiuniversal unfolding of a singularity with the structure of a Frobenius manifold.

He proved the existence of primitive forms in special cases and M. Saito proved their existence in the general case [SM2][SM3]. Using the work of Malgrange [Mal3][Mal5] on deformations of microdifferential systems, M. Saito showed that the choice of a certain filtration on the cohomology of the Milnor fibre yields a primitive form and thus a Frobenius manifold.

This construction of Frobenius manifolds in singularity theory has been quite inaccessible to nonspecialists, because the Gauß–Manin systems are treated using the natural, though sophisticated language of algebraic analysis and especially Malgrange's results require microdifferential systems and certain Fourier–Laplace transforms. This also made it difficult to apply the construction.