There are several good recent textbooks on algebraic geometry at the graduate level, but not (to my knowledge) any designed for an undergraduate course. Humble notes are from a course given in two successive years in the 3rd year of the Warwick undergraduate math course, and are intended as a self-contained introductory textbook.

0. Woffle

Chapter I. Playing with plane curves

 1. Plane conics

 2. Cubics and the group law

Appendix to Chapter I. Curves and their genus

Chapter II. The category of affine varieties

 3. Affine varieties and the Nullstellensatz

 4. Functions on varieties

Chapter Iii. Applications

 5. Projective varieties and birationai equivalence

 6. Tangent space and nonsingularity, dimension

 7. The 27 lines on a cubic surface

 8. Final comments

Index