This chapter lays the foundation of probability theory, which has a central role in statistical mechanics. It starts the exposition with Kolmogorov’s axioms of probability theory and develops the vocabulary through example cases. Some time is spent on sigma algebras and the role they play in probability theory, and more specifically to properly define random variables on the reals. In particular, the popular notion that ‘the probability for a real variable to take on a single value’ is critically analysed and contextualised. Indeed, there are situations in statistical mechanics where some mechanical variables on the reals do get a non-zero probability to take on a single value. Moments and cumulants are introduced, as well as the method of generating functions, which prepare the ground as efficacious tools for statistical mechanics. Finally, Jaynes’s least-biased distribution principle is introduced in order to obtain a priori probabilities given some constraints imposed on the system.