A comprehensive and down-to-earth survey of the theory and practice of extreme value distributions - one of the most prominent success stories of modern applied probability and statistics. Originated by E.J. Gumbel in the early 1940s as a tool for predicting floods, extreme value distributions evolved during the last 50 years of the 20th century into a coherent theory with applications in practically all fields of human endeavour where maximal or minimal values (the so-called extremes) are of relevance. The book should be useful both for a beginner with a limited probabilistic background and to an expert in the field.