This chapter is devoted to the **inverse monodromy problem** for canonical integral and differential systems. The given data for this problem is a mvf

and the objective is either to find a regular canonical integral system with monodromy matrix *U* or a regular canonical differential system with monodromy matrix *U*.

A fundamental theorem of V.P. Potapov (Theorem 2.11) guarantees that both of these problems have at least one solution. In particular, Potapov’s theorem guarantees that there exists a continuous nondecreasing *m × m* mvf *M*(*t*) on an interval [0, *d*] with *M*(0) = 0 such that *U*(λ) is equal to the monodromy matrix

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