Introduction to the Book: Space-Time Random Fields by J.M. Montero, E. Porcu, M. Schlather and G. Fernández-Avilés -- Random Fields Defined on Hilbert Spaces by Hao Zhang -- Some Problems Relating Isotropic Covariance Functions by Michael L. Stein and Emilio Porcu -- Multivariate Random Fields and Robustness in Spatial Statistics by Marc G. Genton -- Spatial and Space-Time Extreme Value Theory for Random Fields by Martin Schlather -- Space-Time Second Order Properties of Random Fields by Emilio Porcu, J.Maria Montero and Gema Fernández-Avilés -- Gaussian Markov Random Fields by Finn Lindgren -- A Journey through non Gaussian Random Fields by Denis Allard -- Space-Time Design for Gaussian Random Fields by Werner Müller -- Simulation of Stochastic Processes and Inference by Maria Dolores Ruiz Medina -- Space Time Point Processes by Thordis Thorarinsdottir.

This book arises as the natural continuation of the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place in Toledo (Spain) in March 2010. This Spring School above all focused on young researchers (Master students, PhD students and post-doctoral researchers) in academics, extra-university research and the industry who are interested in learning about recent developments, new methods and applications in spatial statistics and related areas, and in exchanging ideas and findings with colleagues.