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These lecture notes have been prepared for the BSc Programmernin Actuarial Mathematics under the Department of Mathematical Sciences at thernUniversity Copenhagen, more specifically for the first year course Insurance and lawrn(in Danish: Forsikring og jura). This course introduces the students to conceps andrnmethods from actuarial mathematics, ranging from basic notions of risk to actuarialrnand financial valuation principles, and is deeply formative in nature. While motivatedrnby practical applications, the style of presentation emphasizes mathematical rigor andrnis, consequently, first and foremost targeted a mathematical audience. In particular,rnthe reader is expected to be acquainted with mathematical analysis, including thernnotions of continuity, differentiability, and Riemann integrability as well as thernfundamental theorems of calculus, and well-versed in elementary probability theoryrncorresponding to the material covered in for example Introduction to Probability,rnSecond Edition by Joseph K. Blitzstein & Jessica Hwang (2019).