Gereon Müller (2020). Inflectional morphology in harmonic serialism. (Advances in Optimality Theory.) Sheffield & Bristol, CT: Equinox Publishing. Pp. x + 350.

In Inflectional morphology in harmonic serialism (IMHS), Gereon Müller provides proof of concept for a new theory of the morphology–phonology interface. IMHS proposes a lexicalist (presyntactic), realisational theory of morphology, built around the tenets of Harmonic Serialism (McCarthy 2008): the derivation begins with the root and proceeds through the affixes, whereby the optimal exponent is selected at each step. The monograph goes through a range of data in different languages, developing and refining the theory in order to account for increasingly complex empirical scenarios. The book holds together well. IMHS is a young theory, still finding its bearings in a world full of counterbleeding, multiple exponence and root suppletion. It would be harsh to expect it to provide thorough accounts of many different phenomena. The monograph takes the challenge head on, though, applying the serialist framework to case after case. What we get as a result is the first systematic overview of the theory, delivering more than it originally promised. This achievement makes it possible to dig into the architecture of IMHS, comparing it with other approaches in a way that a theory this novel would not usually facilitate. I devote the first half of this review to outlining IMHS itself (§2), before considering it on its own terms (§3) and highlighting points of contrast with other approaches (§4).