Complex Monge-Ampere Equations are an important class of Partial Differential Equations which are closely related to the Calabi’s conjecture, Kahler-Ricci flow, existence problem of Kahler-Einstein metrics, etc. In this course, students will be guided to read the book/notes “Complex Analytic and Differential Geometry” written by Jean-Pierre Demailly. Topics include the study of plurisubharmonic functions, Stein manifolds, pseudoconvex domain, Lelong numbers, and various important tools in complex geometry such as vanishing theorems and Serre duality. It is expected that students will give regular oral presentations on the subject under the supervision of the instructor. Students should seek the course instructor’s approval to take this course.