Most industrial and natural materials exhibit a macroscopic behaviour which results from the existence of microscale inhomogeneities. The influence of such inhomogeneities is commonly modelled using probabilistic methods. Most of the approaches to the evaluation of the safety of structures according to probabilistic criteria are somewhat scattered. This text attempts to present such material in a coherent and up-to-date form, and also defines the great tasks that must be tackled in coming years. The text is suitable for engineers and researchers dealing with materials, geotechnics, solid mechanics, soil mechanics, statistics and stochastic processes. The expository nature of the book means that no prior knowledge of statistics or probability is required. The book aims to serve as an introduction to the nature of applied statistics and stochastic modelling.