The course will start with the study of local properties of plurisubharmonic funtions in C^n and then move on to the global setting of a compact complex manifold equipped with a Kähler form. The leading character in this story is the complex Monge-Ampere operator. This fully non-linear differential operator is the natural generalization to higher dimensional complex manifolds of the Laplace operator. It plays a central role in various current research areas (Random Polynomials, Complex Dynamics, Kähler-Einstein geometry, Arithmetic (Arakelov) geometry, ...)

Below you can find lecture notes. They appear in the form of "slides" and "expanded lecture notes", where more details are given and where some exercises may be found at the end. OBS! The notes be subject to many updates! More material will appear soon!