Reviewing the historical development of basic algorithms to illuminate the evolution of today's more powerful statistical algorithms, this comprehensive textbook emphasizes recurring themes in all statistical algorithms including computation, assessment and verification, iteration, intuition, randomness, repetition and parallelization, and scalability. Unique in scope, it touches on topics not usually covered in similar books, namely, systematic verification and the scaling of many established techniques to very large databases. Broadly accessible, it offers examples, exercises, and selected solutions in each chapter as well as access to a supplementary website.