Cooperative Optical Non Linearity in a Blockaded Rydberg Ensemble 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 Rydberg excitations opens a new era for quantum optics enabling large single photon non linearity to be accessible in free space for the first time. The thesis describes the theoretical underpinnings of the non linear effect the pioneering experimental results and implications for experiments in the single photon regime.