Independent Random Sampling Methods Introduction Direct methods Accept Reject methods Adaptive rejection sampling methods Ratio of Uniforms Independent sampling for multivariate densities Asymptotically independent samplers Summary and outlook A. Acronyms and abbrevations B. Notation C. Jones RoU generalization D. Polar transformation This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general purpose approaches which can be used to generate samples from arbitrary probability distributions and tailored techniques designed to efficiently address common real world practical problems are introduced and discussed in detail. In turn the monograph presents fundamental results and methodologies in the field elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples which are discussed in detail in the text and supplemented with ready to run computer code. The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field address the latest methods and emphasize the links and interplay between ostensibly diverse techniques