This thesis describes the first demonstration of a cooperative optical non-linearity based on Rydberg excitation. Whereas in conventional non-linear optics the non-linearity arises directly from the interaction between light and matter, in a cooperative process it is mediated by dipole-dipole interactions between light-induced excitations. For excitation to high Rydberg states where the electron is only weakly bound, the dipole-dipole interactions are extremely large and long range, enabling an enormous enhancement of the non-linear effect. Consequently, cooperative non-linear optics using...