Symmetry is evident in many forms from ancient architecture to classical art; however, not as obvious is the mathematical theory of symmetry behind modern applications, such as Rubik's Cube, the art of M.C. Escher, and the security of financial transactions on the Internet. These three topics are not as unrelated as they may initially seem to be. During the lecture, the mathematical ideas behind symmetry will be developed from scratch and illustrated with pictures and numerical examples.