Igor R. Shafarevich, Basic Algebraic Geometry I, second edition, Springer, 1994 (translated by Miles Reid).
I will try to cover the first three chapters and the appendix. Partially depending on the audience, we will do more or less than this. Algebraic Geometry is an important subject and requires a large time investment. I will thoroughly go through the material. The best way to learn this subject is to do many exercises. I plan to have weekly homeworks.