With this book, Jonas Kuhn greatly advances optimality theory (OT) by clarifying the significant choices in the design of a formally precise OT approach to syntax. Building on OT work that uses the representation structures of lexical functional grammar (OT-LFG), Kuhn defines the notion of an OT-syntactic grammar in a declarative, non-derivational way. Along with the standard OT architecture, which is based on a generation metaphor, Kuhn also formalizes parsing-based OT, and goes on to discuss possible combinations of these two architectures. This is followed by an examination of assumptions under which the computational tasks of generation and parsing are decidable for an OT-syntactic grammar.