The course covers a wide range of advanced econometric concepts and methods. In the first part of the course, a theory of weak and partial identification will be presented including some recent advances in these areas. In addition, some modern approaches to sensitivity analysis will be discussed. The second part of the course will introduce students to classical methods and problems of non-parametric estimation. Next the methods for improving estimation and inference in the presence of shape restrictions will be discussed. The final part of the course will discuss econometric models for Industrial Organization. The tools introduced in class will be illustrated with examples from modern economics research.