What is the most descriptively and explanatorily adequate format for syntactic structures and how are they constrained? Different theories of syntax have provided various answers: sets, feature structures, tree diagrams… Building on formal and empirical insights from a wide variety of approaches spanning more than 70 years (including Transformational Grammar, Relational Grammar, Lexical-Functional Grammar, and Tree Adjoining Grammar), this monograph develops a new, mathematically grounded, framework in which objects known as graphs, and the constraints that follow from them, are...