This chapter introduces one of the most powerful tools for understanding the chaotic behavior of dynamical systems, symbolic dynamics. It presents the complicated behavior for certain quadratic functions to what appears at first to be a completely different dynamical system. The chapter also introduces a new level of abstraction involving a “space” of sequences and a mapping on this space that will later serve as a model for the quadratic maps. This abstraction is totally justified when it is shown that iteration of the model mapping can be completely understood. This is in contrast to the quadratic case which is impossible to deal with analytically.