Explore the intricate world of genetic variation in this Oxford Mathematics Public Lecture delivered by Alison Etheridge. Delve into the complex interplay of natural selection, mutation, mating, and other genetic, ecological, and evolutionary mechanisms that shape the patterns of genetic diversity observed today. Discover how modern researchers leverage DNA sequencing data and mathematical models to unravel the mysteries of genetic composition in populations. Learn about the evolution of the field from indirect observations of traits to direct analysis of DNA sequences, and understand the crucial role of mathematical caricatures in interpreting genetic data. Journey through topics such as the Modern Evolutionary Synthesis, family trees, inheritance models, spatial structure in populations, and the application of equations like Wright-Malécot, Allen-Cahn, and Cahn-Hilliard in studying genetic patterns across various scales.