This book, "Non-Uniform Random Variate Generation" by Luc Devroye, is a comprehensive treatise on the generation of non-uniform random variates, a field that bridges statistics, operations research, and computer science. The author emphasizes the importance of random numbers in various applications, such as statistical testing, large-scale simulations, and algorithm comparisons. The book covers a wide range of topics, including the expected complexity of random variate generation algorithms, the inversion method, the rejection method, decomposition into discrete mixtures, and specialized algorithms for generating various distributions. It also delves into discrete and continuous random variates, multivariate distributions, random sampling, and random combinatorial objects. The text is structured into several chapters, each focusing on specific methods and techniques, and includes numerous exercises to reinforce understanding. The book is based on course notes from McGill University and benefited from feedback from various contributors, reflecting a labor of love and extensive research.This book, "Non-Uniform Random Variate Generation" by Luc Devroye, is a comprehensive treatise on the generation of non-uniform random variates, a field that bridges statistics, operations research, and computer science. The author emphasizes the importance of random numbers in various applications, such as statistical testing, large-scale simulations, and algorithm comparisons. The book covers a wide range of topics, including the expected complexity of random variate generation algorithms, the inversion method, the rejection method, decomposition into discrete mixtures, and specialized algorithms for generating various distributions. It also delves into discrete and continuous random variates, multivariate distributions, random sampling, and random combinatorial objects. The text is structured into several chapters, each focusing on specific methods and techniques, and includes numerous exercises to reinforce understanding. The book is based on course notes from McGill University and benefited from feedback from various contributors, reflecting a labor of love and extensive research.