This is a course in the foundations of statistical inference techniques. Assuming some prior exposure to foundational & intermediate statistical methods, this course will first cover topics such as Kolgomorov’s axioms of probabilities, basics of set theory, discrete combinatorial probability, Bayes’ theorem, probability distributions & their properties & assumptions of dependence & independence. These topics are followed by the foundational topics of statistics: sampling distributions, the law of large numbers & the central limit theorem. This course will mix theoretical approaches with simulation-based illustrations of these main topics. The student will be expected to understand the mathematical theory & apply the topics covered to problem solving via analytical & simulation based methods in statistical programming language such as R.