This book presents notions and ideas from the foundations of a statistical treatment of risks. Bayesian methods are frequently used in that area, hence a reasonable proportion of the presentation is devoted to such approaches. Modern statistical tools, namely Poisson regression, analysis of deviance, extreme-value theory and threshold methods are also used to identify and solve practical problems. The knowledge of such tools facilitates the understanding of the role of probability in risk analysis and proper use of outputs given by software packages. The book is written with a student in mind who has studied elementary undergraduate courses in engineering mathematics, perhaps including an introductory course in statistics. The text emphasizes an understanding of the theory and methods presented. Hence, comments are given verbally and an intuitive reasoning is frequent. This is not just another new textbook on elementary probability and statistics, but focuses strongly on applications within the field of risk and safety analysis.