The course aims (i) to present the fundamentals of Mathematical Population Genetics, which gives mathematical expression to the genetic aspects of evolution in natural populations, and (ii) to present some of the ideas from Evolutionary Game Theory that have recently been used to illuminate the evolution of various properties and behaviours of animals. The course introduces a wide range of new mathematical models which include both continuous and discrete-time systems. The generality of the key models enables us to prove a range of theorems that yield important and fundamental results in both mathematical genetics and game theory.