In modern medicine, mathematical modeling and statistical (big) data analysis are playing an increasingly important role to uncover complex disease mechanisms. In this course, we undertake an excursion into the world of quantitative biomedical research and discover a range of fascinating mathematical principles that govern human health and disease. Based on a series of concrete research topics we will learn how to critically read the biomedical literature and develop our own hypotheses. We will translate biomedical problems into the language of mathematics and tackle them using a combination of analytic reasoning and data analysis. Course topics will include a selection of the following: cardiology, immune system and infectious diseases, evolutionary game theory, cancer evolution, global and population health. This course has a substantial research component. As such, particular emphasis will be placed on mathematical reasoning, problem solving and the effective communication of scientific ideas, both through writing and oral presentations. The overarching goal of this course is to dive head-first into the exciting world of research at the interface of mathematics and medicine.