Coalescent Theory provides the foundation for molecular population genetics and genomics. It is the conceptual framework for studies of DNA sequence variation within species, and is the source of essential tools for making inferences about mutation, recombination, population structure and natural selection from DNA sequence data. This monograph is intended mainly for biologists but it will also be of interest to mathematicians who wish to see how this branch of applied probability theory plays out in a biological setting. Contents: 1 Gene Genealogies and Genetic Data; 2 Probability Theory for the Coalescent; 3 The Coalescent; 4 Neutral Mutations and Genetic Polymorphisms; 5 Population Structure; 6 Splitting Lineages: Recombination and Weak Selection; 7 Separation of Time Scales and Robustness Results; 8 Simulations and Simulation-based Methods; Solutions to Odd-Numbered Exercises; Bibliography; Index.