The study of the statistics of extreme events is an essential first step in the mitigation of natural catastrophies. This book reviews the theoretical and practical aspects of the statistics of extreme events in nature. Topics range from high and low flows, to earthquakes and volcanic eruptions, land slides, avalanches, windstorms, extreme sea levels and high waves, forest fires and other disasters that threaten lives and properties and often cause severe economic losses worldwide. In many applications it is important to consider extreme events in a bivariate or multivariate context. Copulas exactly describe and model the dependence structure between random variables independently of the marginal laws involved. This approach simplifies the analysis of phenomena involved and makes it possible to introduce new parameters for the characterization of the extreme behaviour of a system.