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

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