Book excerpt: This accessible text/reference presents a coherent overview of the emerging field of non-Euclidean similarity learning. The book presents a broad range of perspectives on similarity-based pattern analysis and recognition methods, from purely theoretical challenges to practical, real-world applications. The coverage includes both supervised and unsupervised learning paradigms, as well as generative and discriminative models. Topics and features: explores the origination and causes of non-Euclidean (dis)similarity measures, and how they influence the performance of traditional classification algorithms; reviews similarity measures for non-vectorial data, considering both a “kernel tailoring” approach and a strategy for learning similarities directly from training data; describes various methods for “structure-preserving” embeddings of structured data; formulates classical pattern recognition problems from a purely game-theoretic perspective; examines two large-scale biomedical imaging applications.