Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages.

Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory.

This book is accessible to graduate students and researchers with basic knowledge in probability theory and, partly, in point processes and Gaussian processes. The required statistical prerequisites are minimal.

Since the publication of the first edition of this seminar book, the theory and applications of extremes and rare events have seen increasing interest. Laws of Small Numbers gives a mathematically oriented development of the theory of rare events underlying various applications. The new edition incorporates numerous new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.

I. The IID Case: Functional Laws of Small Numbers.- 1 Functional Laws of Small Numbers.- 2 Extreme Value Theory.- 3 Estimation of Conditional Curves.- II. The IID Case: Multivariate Extremes.- 4 Basic Theory of Multivariate Maxima.- 5 Multivariate Extremes: The Pickands Approach.- 6 The Pickands Approach in the Bivariate Case.- 7 Multivariate Extremes: Supplementary Concepts and Results.- III. Non IID Observations.- 8 Introduction to the Non IID Case.- 9 Extremes of Random Sequences.- 10 Extremes of Gaussian Processes.- 11 Extensions for Rare Events.- 12 Statistics of Extremes.- Author Index.