In this chapter, we will explain what the flow equivalence of topological Markov shifts is. Two discrete dynamical systems are said to be flow equivalent if they are realized as discrete dynamical systems of cross sections of a common continuous flow space. Franks’s theorem describing that the pair of the Bowen–Franks group \(\operatorname {BF}(A)\) and the Parry–Sullivan determinant \({{\operatorname {det}}}(I - A)\) is a complete set of invariants of flow equivalence of irreducible topological Markov shifts is proved.