Zariski Geometries: Geometry from the Logician's Point of View (London Mathematical Society Lecture Note Series, Series Number 360)

This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Its logical approach helps us understand why algebraic geometry is so fundamental throughout mathematics and why the extension to noncommutative geometry, which has been forced by recent developments in quantum physics, is both natural and necessary. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.

Boris Zilber is Professor of Mathematical Logic in the Mathematical Institute at the University of Oxford.