Phylogenetics is a growing area of research. Phylogenies (phylogenetic trees and networks) allow biologists to study and graph evolutionary relationships between different species. These are also used to investigate other evolutionary processes, including how languages developed or how different strains of a virus are related to each other. This self-contained book addresses the underlying mathematical theory behind the reconstruction and analysis of phylogenies. The theory is grounded in classical concepts from discrete mathematics and probability theory as well as techniques from other branches of mathematics (algebra, topology, differential equations). The biological relevance of the results is highlighted throughout, and the author supplies both proofs of classical theorems and results not covered in existing books. Relevant mathematical results derived over the past twenty years are emphasised, and numerous exercises, examples and figures are provided. The book will be ideal for any applied mathematician, biomathematician, discrete mathematician, systematic biologist, or computer scientist specialising in algorithms or bioinformatics.