It was more than ten years ago that an original version of this monograph was published with the title Quantum Optics in Japanese from Iwanami Shoten in Tokyo. Therefore, making the best use of this chance to translate the book into an English version, we have tried to include the exciting developments of the relevant subjects in these ten years, especially novel nonlinear optical responses of materials. The ?rst example of these nonlinear optical phen- ena is laser cooling and subsequent observation of Bose¿Einstein and Fermi condensation of neutral atoms. Second, it is now possible to generate f- tosecond laser pulses. Then higher-harmonics in the extreme ultraviolet and soft X-ray regions and higher-order Raman scattering can be generated by irradiating these ultrashort laser pulses on atomic and molecular gases and crystals. These multistep signals are applied to the generation of attosecond laser pulses. Third, interference e?ects of the second harmonics are used to observe the ferroelectric and antiferromagnetic domain structures of crystals with a strongly correlated electronic system. These novel nonlinear optical phenomena could not be treated without the quantized radiation ?eld. We already have classical textbooks treating, individually, the quantum theory of the radiation ?eld and nonlinear optics. Taking account of these situations, we have described these exciting nonlinear optical responses as well as laser oscillation and supperradiance, based upon the quantum theory of the radiation ?eld. At the same time, we have changed the title of this monograph toQuantum Nonlinear Optics.