Basic Algebraic Geometry 1

I. Basic Notions.- 1. Algebraic Curves in the Plane.- Exercises to §1.- 2. Closed Subsets of Affine Space.- Exercises to §2.- 3. Rational Functions.- Exercises to §3.- 4. Quasiprojective Varieties.- Exercises to §4.- 5. Products and Maps of Quasiprojective Varieties.- Exercises to §5.- 6. Dimension.- Exercises to §6.- II. Local Properties.- 1. Singular and Nonsingular Points.- Exercises to §1.- 2. Power Series Expansions.- Exercises to §2.- Exercises to §3.- 4. The Structure of Birational Maps.- Exercises to §4.- 5. Normal Varieties.- Exercises to §5.- 6. Singularities of a Map.- Exercises to §6.- III. Divisors and Differential Forms.- 1. Divisors.- Exercises to §1.- 2. Divisors on Curves.- Exercises to §2.- 3. The Plane Cubic.- Exercises to §3.- 4. Algebraic Groups.- Exercises to §4.- 5. Differential Forms.- Exercises to §5.- 6. Examples and Applications of Differential Forms.- Exercises to §6.- IV. Intersection Numbers.- 1. Definition and Basic Properties.- Exercises to §1.- 2. Applications of Intersection Numbers.- Exercises to §2.- 3. Birational Maps of Surfaces.- Exercises to §3.- 4. Singularities.- Exercises to §4.- Algebraic Appendx.- References.