There are many excellent resources available on classical algebraic geometry. (With the exception of Mumford's book, the following are available from either the author's web page or through the CSU library.) During the semester, I will be closely consulting:

• David Mumford, Algebraic Geometry I: complex projective varieties.
• James Milne, (Basic First Course in) Algebraic Geometry.

Additional relevant textbooks:

• I.R. Shafarevich, Basic algebraic geometry 1: Varieties in Projective Space.