There are many nice books on Algebraic Geometry, often with different points of view on the subject.

The text for the course is Algebraic Geometry: A First Course by J. Harris, Springer Graduate Texts in Mathematics 133, ISBN 0-387-97716-3. This is a very geometric book starting from some of the classical algebraic varieties which motivated the origins of the subject. This book has many exercises and examples that are useful in getting a feel for algebraic geometry. Here is an excerpt from the Mathematical Reviews discussion of the book:

"... the book succeeds brilliantly ... by concentrating on a number of core topics .... and by treating them in a hugely rich and varied way..."

Read the whole review at the AMS math reviews site.

The following books, as well as a copy of the text, are on reserve in the Mathematics Library in Hill Center:

- Algebraic Geometry, R. Hartshorne
- This book is a canonical reference to the general theory
- Basic algebraic geometry, I. R. Shafarevich
- Ideals, varieties and algorithms, D. Cox et al
- Using Algebraic Geometry, D. Cox et al
- Complex projective varieties I, D. Mumford
- Principles of Algebraic Geometry, P. Griffiths and J. Harris
- This deals with the theory of complex varieties by using the topology and
differential geometry of complex manifolds
- Elementary algebraic geometry, K. Kendig
- Introduction to commutative algebra, M. F. Atiyah and I. G. MacDonald
- Introduction to algebraic geometry, J. Semple
- Schemes : the language of modern algebraic geometry , D. Eisenbud, J. Harris
- Commutative algebra with a view toward algebraic geometry,D. Eisenbud
- Algebraic
geometry notes of J. Milne's University of Michigan course