NB: most documents are in pdf format. You might need Acrobat Reader (which is free to download) to view it. Some version of GhostView also works.
Lecture 1: Review on compact Riemann surfaces/ algebraic curves.
Lecture 2: Affine varieties and projective varieties.
Lecture 3: Divisors.
Lecture 4: Linear series and maps to projective spaces.
Here is some part of Lazarsfeld's Positivity in Algebraic Geometry, which defines divisors and linear series. Laz1.ps (It's in postscript, you might need GhostView)
Lecture 5: Sheaves cohomology.
Lecture 6: Bertini's theorem, Ampleness Criterion, Intersection theory and Riemann-Roch theorem on surfaces.
Lecture 7: Hodge Index Theorem
Lecture 8: Blowing-up and Blowing-down
Lecture 9: Birational maps and minimal models
Lecture 10: Minimal model program for surfaces
Lecture 11: rational surfaces
Lecture 12: ruled surfaces
hw1 hw2 hw3 hw4