This course aims at introducing students to advanced mathematical methods for modeling and statistical inference in economic analysis. The course builds on the classical foundations of statistics (model specification, parameter estimation, hypothesis testing) and extends the framework to address questions which are of primary importance in econometric analysis, like: How can we estimate the parameters in an equilibrium model for demand and supply of a good? What can we learn from a statistical model which is only an approximation of reality? How can we estimate the parameters of a structural economic model with rational agents optimizing intertemporally their utility? The course is structured in three chapters: (1) Least squares methods (endogeneity, Instrumental Variables, Systems of Simultaneous Equations); (2) Nonlinear regression methods (M-estimators, Pseudo Maximum Likelihood theory); (3) The Generalized Method of Moments (rational expectations models, Euler conditions and orthogonality conditions).