You can find symmetry in physics, chemistry, biology, anthropology, quantum mechanics and just about every other field you can think of. Symmetry is often used to simplify problems in all of these fields, it allows you to study the simpler parts of a system and piece them together to understand the whole picture. Group theory is the mathematical study of symmetry. We will discuss some natural places where groups of symmetries appear in mathematics and the natural sciences and then we will move on to discuss how mathematicians like to think about and study groups of symmetries in general.