This book is an introduction to or refresher course in higher mathematics for practitioners of digital humanities. Its purpose is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. It should enable humanist scholars to address complicated technical material with confidence. The individual subjects we tackle are (in order): logic and proof, discrete mathematics, abstract algebra, probability and statistics, calculus, and differential equations. This is not at all the order in which these subjects are usually taught in school curricula, and indeed, it is possible to take a course of study that does not include all of them. Our ordering is borne of our own sense of how best to convey the concepts of mathematics to humanists, and is, like mathematics itself, strongly cumulative.