Functional Laws of Small Numbers.- ExtremeValueTheory.- Estimation of Conditional Curves.- Basic Theory of Multivariate Maxima.- Multivariate Extremes: The Pickands Approach.- The Pickands Approach in the Bivariate Case.- Multivariate Extremes: Supplementary Concepts and Results.- Introduction to the Non IID Case.- Extremes of Random Sequences.- Extremes of Gaussian Processes.- Extensions for Rare Events.- Statistics of Extremes.