The field of distribution-free inference seeks to provide robust, universally valid statistical guarantees that do not depend on modeling assumptions. Such techniques are ideal when used in conjunction with modern machine learning algorithms too complex to be analyzed with traditional statistical methods. Conformal prediction is a popular technique within this field, quantifying the uncertainty of predictions produced by arbitrary algorithms without relying on any assumptions or special structure of the prediction algorithm or dataset. This book offers a rigorous exposition of the mathematical ideas that underlie conformal prediction, foregrounding key theoretical results and proofs. Numerous theoretical and methodical extensions address problems such as computational efficiency, distribution shift, and streaming data. The text also presents a distribution-free perspective on statistics questions such as regression and conditional independence testing. This is a valuable resource for academic researchers, practitioners and graduate students alike. This title is also available as open access on Cambridge Core.