Includes illustrations, bibliographic references and subject index.

Grothendieck's beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

- Written by two highly respected mathematicians who are also bestselling Springer authors
- Fills the gap between books on classical algebraic geometry and full-blown accounts of the theory of schemes
- Provides a simple account, emphasizing and explaining the universal geometric concepts behind the definitions
- Explicit calculations show how scheme theory is utilized in practice
- Discusses applications to number theory, physics, and applied mathematics