This book is a fundamental introduction to the mathematical methods of German private health insurance. It focuses on topics such as actuarial principles, premium calculation, and aging reserves. Important developments in recent years, such as the portability of aging reserves and unisex tariffing, are also presented. While the application of the results is emphasized, there is a strong emphasis on appropriate mathematical rigor. Numerous practical examples and exercises with solution hints make the book a helpful companion in studies, actuarial training, and professional practice.