Abstract: Have you ever wondered about the meaning of the phrase "survival of the fittest"? To an evolutionary biologist, fitness simply means reproductive success and reflects how well an organism is adapted to its environment. How systems adapt over time has been a central question in Biology and other Life-Sciences. While I will focus on the theory of Adaptive Dynamics, there are many areas of mathematics that have contributed to our understanding of adaptation. In this talk, I will give an overview of how we can use mathematical models to understand adaptation as an evolutionary process and its relationship to creating and preserving diversity. If time permits, I will also address the connections between this theory and my own research in disease modeling.