This book presents notions and ideas at the foundations of a statistical treatment of risks. The text is unlike that found in traditional mathematics literature and differs from typical textbooks in its verbal approach to many explanations and examples. The text is written for students who have studied elementary undergraduate courses in engineering mathematics, perhaps including a minor course in statistics. The focus is on statistical applications within the field of engineering risk and safety analysis. Coverage includes Bayesian methods. 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.