The course addresses foundational topics in statistical inference and regression analysis. It aims to provide graduate students who wish to use quantitative methods in their research with rigorous foundations of probability theory, statistical inference, and multivariate regression analysis. The emphasis is given to acquiring rigorous theoretical foundations, which are necessary to learn and apply state-of-the-art quantitative analyses in the discipline. PhD students who wish to use quantitative methods in their dissertation research are expected to take this course. Along with a mathematical introduction to various methods, their application through the use of statistical computer packages is also part of the course.