The statistical analysis of extreme data is important for various disciplines, including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to the parametric modeling, exploratory analysis and statistical interference for extreme values.The entire text of this third edition has been thoroughly updated and rearranged to meet the new requirements. Additional sections and chapters, elaborated on more than 100 pages, are particularly concerned with topics like dependencies, the conditional analysis and the multivariate modeling of extreme data. Parts IIII about the basic extreme value methodology remain unchanged to some larger extent, yet notable are, e.g., the new sections about 'An Overview of Reduced-Bias Estimation' (co-authored by M.I. Gomes), 'The Spectral Decomposition Methodology', and 'About Tail Independence' (co-authored by M. Frick), and the new chapter about 'Extreme Value Statistics of Dependent Random Variables' (co-authored by H. Drees). Other new topics, e.g., a chapter about 'Environmental Sciences', (co--authored by R.W. Katz), are collected within Parts IVVI.