'Phylogenetics' is the reconstruction and analysis of phylogenetic (evolutionary) trees and networks based on inherited characteristics. It is a flourishing area of intereaction between mathematics, statistics, computer science and biology. The main role of phylogenetic techniques lies in evolutionary biology, where it is used to infer historical relationships between species. However, the methods are also relevant to a diverse range of fields including epidemiology, ecology, medicine, as well as linguistics and cognitive psychology This book is intended for biologists interested in the mathematical theory behind phylogenetic methods, and for mathematicians, statisticians, and computer scientists eager to learn about this emerging area of discrete mathematics. 'Phylogenetics' in the 24th volume in the Oxford Lecture Series in Mathematics and its Applications. This series contains short books suitable for graduate students and researchers who want a well-written account of mathematics that is fundamental to current to research. The series emphasises future directions of research and focuses on genuine applications of mathematics to finance, engineering and the physical and biological sciences.