The aim of phylogenetic analysis is to reconstruct the phylogeny (evolutionary history) of a set of organisms from present-day data. Think of this as predicting the past from the present. One might suspect that this is not easy - for one, it is harder to evaluate the results of predictions than if one were predicting the future. Despite the inherent difficulties, phylogeneticists (those who try to reconstruct phylogenies for a living) are finding computational methods to be very useful in cutting through the space of exponentially-many phylogenies and generating a handful of plausible phylogenies. This short book presents the main computational methods in present use in this field, as well as some on the cutting edge. These methods are presented in the setting of building binary trees (rooted or unrooted) from molecular sequence data. Some of these methods are applicable to other types of data as well. This book is written from the quantitative perspective. The aim is to present the algorithms and ideas in sufficient depth and at a formal level for an informatician to be able to implement them or even adapt them. This book may also be used in a graduate or upper-division undergraduate course on the topic (one in which the computational perspective is emphasized) or as an adjunct in a course on bioinformatics. The first chapter is on substitution models, stochastic processes, and substitution matrices, the second on distance-based tree-building methods, the third on parsimony-based tree-building methods, the fourth on probabilistic tree-building methods, and the fifth on finding consensus features in built trees. The sixth and the seventh chapters present more cutting edge material,on sequence graphs, on aligning sequence graphs, and on building phylogenetic trees from unaligned sequences using these ideas.