This is a classical course in the theory of probability - the branch of mathematics that quantifies uncertainty. The course provides an initial review of concepts in elementary probability, before moving to a detailed exploration of the notions of density, distribution and moment for discrete and continuous random variables. Various case study examples are used to show how these ideas can be used in solving real-world problems. Finally, asymptotic theory is presented, with an illustration of the use of the Weak Law of Large Numbers and the central limit theorem in sampling technique and approximation.