This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. The stakes are high and the reader determines the outcome. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. This works in conjunction with the bayess package.Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels, as exemplified by courses given at Université Paris Dauphine (France), University of Canterbury (New Zealand), and University of British Columbia (Canada). It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics. A strength of the text is the noteworthy emphasis on the role of models in statistical analysis.This is the new, fully-revised edition to the book Bayesian Core: A Practical Approach to Computational Bayesian Statistics.Jean-Michel Marin is Professor of Statistics at Université Montpellier 2, France, and Head of the Mathematics and Modelling research unit. He has written over 40 papers on Bayesian methodology and computing, as well as worked closely with population geneticists over the past ten years.Christian Robert is Professor of Statistics at Université Paris-Dauphine, France. He has written over 150 papers on Bayesian Statistics and computational methods and is the author or co-author of seven books on those topics, including The Bayesian Choice (Springer, 2001), winner of the ISBA DeGroot Prize in 2004. He is a Fellow of the Institute of Mathematical Statistics, the Royal Statistical Society and the American Statistical Society. He has been co-editor of the Journal of the Royal Statistical Society, Series B, and in the editorial boards of the Journal of the American Statistical Society, the Annals of Statistics, Statistical Science, and Bayesian Analysis. He is also a recipient of an Erskine Fellowship from the University of Canterbury (NZ) in 2006 and a senior member of the Institut Universitaire de France (2010-2015).