This text presents notions and ideas at the foundations of a statistical treatment of risks. Such knowledge facilitates the understanding of the influence of random phenomena and gives a deeper understanding of the possibilities offered by and algorithms found in certain software packages. Since Bayesian methods are frequently used in this field, a reasonable proportion of the presentation is devoted to such techniques. The text is written with a student in mind who has studied elementary undergraduate courses in engineering mathematics, maybe including a minor course in statistics. Despite employment of the style of presentation traditionally found in the mathematics literature (including descriptions like definitions, examples, etc.). Probability and Risk Analysis emphasizes an understanding of the theory and methods presented; hence, comments are given verbally and a reasoning is frequent. With respect to the contents (and its presentation), the ambition has not been to write just another new textbook on elementary probability and statistics. There are lots of such books, but instead the focus is on applications within the field of risk and safety analysis.