This course is intended to serve as a rigorous introduction to probability theory and statistical methods for PhD students whose training in these areas may fall short of meeting the pre-requisites for the 2nd-semester core Advanced Research Methods course. The course begins by introducing modern algebraic and graphical tools (both parametric and nonparametric) used to describe key features of raw batches of data (descriptive statistics) then develops several lines of probabilistic thinking (frequentist, information-theoretic, and Bayesian) for understanding how the data were generated. We move on from there to develop competing ways to draw inferences about the nature of the population, or of the “data generating process”, from which the data in hand originated. This entails reflecting on alternative sampling designs, hypothesis formulation and testing, and weighing evidence to draw inferences that go beyond the sample evidence (inferential statistics). With that foundation, we devote significant time to the theory and practice of ordinary least squares (OLS) regression, the most widely used instrument in the policy analyst’s statistical tool box. We conclude the course with a treatment of important extensions of OLS regression that employ maximum likelihood, or information-theoretic, methods to draw inferences about causal linkages among observable variables and to make qualified predictions about future outcomes.