The statistical analysis of extreme data is important for various disciplines, including insurance, finance, hydrology, engineering and environmental sciences. This book is an introduction to parametric modelling, exploratory analysis and statistical inference for extreme events. The text contains special chapters about insurance (co-authored by M. Radtke), returns in asset prices (co-authored by C.G. de Vries) and flood frequency analysis, as well as five longer case studies. XTREMES, an interactive menu-driven system which runs under Windows 3.1 (16 bit version) and Windows 95, NT (32 bit version) is included, and is designed to facilitate the assessment of the adequacy of the parametric modelling and the statistical inference. It contains an integrated Pascal-like programming language.