I will begin from some preliminaries of algebraic geometry, then establish the intersection theory on surfaces. In the series of talks, I will try to include: Hodge index theory, Riemann-Roch theorem and Noether's formula, blow-ups, elimination of indeterminacy, factorization of birational morphisms, ruled surfaces and rational surfaces, examples, Castelnuovo's rationality criterion, Kodaira dimension and classification of surfaces. Here is a rough table of contents for the lectures:
 

• Picard group and intersection theory
• Numerical invariants and some general theorems on algebraic surfaces
• Birational map and minimal model of surfaces
• Ruled surfaces and rational surfaces
• Castelnuovo's rationality criterion
• Kodaira dimension and classification