Positivity in Algebraic Geometry

0) Basic notions: fiber bundles, divisors, morphisms; linear, algebraic and numerical equivalence; fundamentals of intersection theory.
1) Ampleness and nefness: basic definitions; the various classical characterizations of ampleness (cohomological via Serre vanishing and bundle-theoretic via global generation); Nakai-Moishezon criterion for amplitude; an intersection theoretic characterization of nefness via Kleiman's theorem; Q- and R-divisors; the cone of effective curves; Kleiman's criterion for ampleness via cones of divisors and curves; Hodge index type inequalities.
2) Bigness: Iitaka's theorem on morphisms induced by linear systems; definition of Iitaka and Kodaira dimensions; definition of bigness and pseudo-effectiveness; the cone of big and pseudo-effective divisors; the volume function and its properties; finite generation of rings of sections and Zariski's criterion.
3) Introduction to the ideas of higher-dimensional birational geometry: a survey of ideas/techniques/results of the last 50 years on birational classification of algebraic varieties over the complex numbers.