In this book, Matilde Marcolli, Noam Chomsky, and Robert C. Berwick prove that Merge can be described as a very particular kind of highly structured algebra. Additionally, the book shows how Merge can be placed within a consistent framework that includes both a syntactic-semantic interface that realizes Chomsky’s notion of a conceptual-intentional interface, and an externalization system that realizes language-specific constraints. The syntax-semantics interface encompasses many current semantical theories and offers deep insights into the ways that modern “large language models” work, proving that these do not undermine in any way the scientific theories of language based on generative grammar.