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This book provides exact analytical solutions to some of the most challenging and exciting problems in quantum optics, ranging from the theory of multi-level atom-radiation field interaction to multi-photon parametric processes in non-linear quantum optics. The problems are generally reduced to two-state dynamics for which detailed reader-friendly solution procedures displaying every important mathematical step are presented. The exact discrete and equivalent continuous variable time evolution operators generate explicitly specified time evolving spin / helicity coherent state vectors and Schroedinger wave functions describing the general quantum states of light, including dissipative dynamics. Photon polarization state dynamics under semi-classical and fully quantized parametric interactions is clearly presented. All the results in fully quantized parametric processes in non-linear quantum optics are new and are appearing for the first time in the literature. The book is particularly useful for graduate level teaching and as a resource text for research in linear and non-linear quantum optics.