Coalescent theory tells us what gene genealogies are expected to look like if populations have different demographic histories - i.e, population size, structure, etc. The aim of this book is to provide an accessible introduction to Coalescent Theory with a view towards data analysis. Coalescent Theory has in the last two decades moved from being an obscure technique that appealed to mathematical population geneticists to a central tool in data analysis of DNA sequences. The completion of the sequencing of the human genome and accompanying determination of SNPs and haplotypes will increase its importance even further. This textbook, rich in examples and illustrations, is suitable for a graduate course in statistics, population-, molecular-, and medical genetics.