Decades ago, Mumford wrote that algebraic geometry “seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics.”

The revolution has now fully come to pass and has fundamentally changed how we think about many fields of mathematics.

This book provides a thorough foundation in the powerful ideas that now shape the landscape, with an informal yet rigorous exposition that builds intuition for the formidable machinery.