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.

I Basic Definitions.- II Examples.- III Projective Schemes.- IV Classical Constructions.- V Local Constructions.- VI Schemes and Functors.- References.- Index.