The construction of Frobenius manifolds for singularities is due to K. Saito and M. Saito, using results of Malgrange. The version presented in section 11.1 replaces the use of Malgrange's results by the solution of the Riemann–Hilbert–Birkhoff problem in section 7.4 and by the tools in section 8.2. All the other ingredients from the Gauß–Manin connection are provided in chapter 10.

Section 11.2 establishes series of functions which are close to Dubrovin's deformed flat coordinates. Some use of them is made in chapter 12. In view of some results of Dubrovin, Zhang, and Givental one can hope that much more can be found in these series of functions.

Sabbah generalized most of K. Saito and M. Saito's construction to the case of tame functions with isolated singularities on affine manifolds [Sab3][Sab2] [Sab4]. But the details are quite different, there one uses oscillating integrals, and the results are not as complete as in the local case. We discuss this at some length in section 11.4.

The case of tame functions is important for the following question within mirror symmetry: Are certain Frobenius manifolds from quantum cohomology isomorphic to certain Frobenius manifolds somehow coming from functions with isolated singularities? This is motivated by the results of Givental. A special case was looked at by Barannikov. In section 11.3 we make some remarks about this version of mirror symmetry.