This book discusses the probability distributions used in reliability engineering and risk analysis. For each distribution, the book provides graphical visualization and related formulas, along with the corresponding reliability functions and other related formulas. Common statistics such as moments and confidence interval formulas are presented, including the likelihood functions. For the most important distributions, the book provides derivation of the maximum likelihood estimates. Bayesian estimations using non-informative and conjugate priors are provided, followed by a discussion on the distribution characteristics and applications to reliability engineering. The book includes numerical examples for each distribution, demonstrating applications of the distribution function in the context of reliability engineering and risk analysis problems. Each section concludes with online resources and hardcopy references for further information, followed by the relationship of each distribution to other distributions.