Markov Models in Molecular Evolution -- to Applications of the Likelihood Function in Molecular Evolution -- to Markov Chain Monte Carlo Methods in Molecular Evolution -- Population Genetics of Molecular Evolution -- Practical Approaches for Data Analysis -- Maximum Likelihood Methods for Detecting Adaptive Protein Evolution -- HyPhy: Hypothesis Testing Using Phylogenies -- Bayesian Analysis of Molecular Evolution Using MrBayes -- Estimation of Divergence Times from Molecular Sequence Data -- Models of Molecular Evolution -- Markov Models of Protein Sequence Evolution -- Models of Microsatellite Evolution -- Genome Rearrangement -- Phylogenetic Hidden Markov Models -- Inferences on Molecular Evolution -- The Evolutionary Causes and Consequences of Base Composition Variation -- Statistical Alignment: Recent Progress, New Applications, and Challenges -- Estimating Substitution Matrices -- Posterior Mapping and Posterior Predictive Distributions -- Assessing the Uncertainty in Phylogenetic Inference.In the field of molecular evolution, inferences about past evolutionary events are made using molecular data from currently living species. With the availability of genomic data from multiple related species, molecular evolution has become one of the most active and fastest growing fields of study in genomics and bioinformatics. Most studies in molecular evolution rely heavily on statistical procedures based on stochastic process modelling and advanced computational methods including high-dimensional numerical optimization and Markov Chain Monte Carlo. This book provides an overview of the statistical theory and methods used in studies of molecular evolution. It includes an introductory section suitable for readers that are new to the field, a section discussing practical methods for data analysis, and more specialized sections discussing specific models and addressing statistical issues relating to estimation and model choice. The chapters are written by the leaders in the field and they will take the reader from basic introductory material to the state-of the-art statistical methods. This book is suitable for statisticians seeking to learn more about applications in molecular evolution and molecular evolutionary biologists with an interest in learning more about the theory behind the statistical methods applied in the field. The chapters of the book assume no advanced mathematical skills beyond basic calculus, although familiarity with basic probability theory will help the reader. Most relevant statistical concepts are introduced in the book in the context of their application in molecular evolution, and the book should be accessible for most biology graduate students with an interest in quantitative methods and theory. Rasmus Nielsen received his Ph.D. form the University of California at Berkeley in 1998 and after a postdoc at Harvard University, he assumed a faculty position in Statistical Genomics at Cornell University. He is currently an Ole Rømer Fellow at the University of Copenhagen and holds a Sloan Research Fellowship. His is an associate editor of the Journal of Molecular Evolution and has published more than fifty original papers in peer-reviewed journals on the topic of this book.