This book considers evolution at different scales: sequences, genes, gene families, organelles, genomes and species. The focus is on the mathematical and computational tools and concepts, which form an essential basis of evolutionary studies, indicate their limitations, and give them orientation. Recent years have witnessed rapid progress in this area, with models and methods becoming more realistic, powerful, and complex. This book of contributed chapters is authored by renowned scientists and covers recent results in the highly topical area of mathematics in evolution and phylogeny. Each chapter is a detailed overview of a specific topic, from the underlying concepts to the latest results. Aimed at graduates and researchers in phylogenetics, this book will be of interest to both mathematicians and biologists.