This book is the first dedicated to linguistic parsing - the processing of natural language according to the rules of a formal grammar - in the Minimalist Program. While Minimalism has been at the forefront of generative grammar for several decades, it often remains inaccessible to computer scientists and others in adjacent fields. This volume makes connections with standard computational architectures, provides efficient implementations of some fundamentalminimalist accounts of syntax, explores implementations of recent theoretical proposals, and explores correlations between posited structures and measures of neural activity during human language comprehension. These studies will appeal to graduate students and researchers in formal syntax, computationallinguistics, psycholinguistics, and computer science.