Analysis and simulation of multivariate and spatial extremes

The thesis consists of eight articles that have been published recently in various scientific journals. It contains contributions to the theory and statistics of max-stable processes including their representation (Chapter 2), likelihood-based inference (Chapter 3), unconditional simulation (Chapters 4, 5 and 6) and conditional simulation with applications to downscaling and statistical post-processing (Chapters 7. 8 and 9). Brief overviews over the main results in these areas and the author's contributions will be given in an introductory chapter.