This chapter defines random variables as measurable functions in a probability space, their distributions, (cumulative) distribution functions, and (eventually) densities. It covers the most important probability distributions, including one point, two-point, multinomial, geometric, negative binomial (Pascal), hypergeometric, uniform on a set (interval), exponential, Gamma, beta, Cauchy, and Gaussian (normal) distributions. Additionally, singular probability measures and the Lebesgue Decomposition Theorem are discussed. In the context of independent random variables, independence is explained using the language of multidimensional distribution and convolutions are defined.