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.