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