"The objective of this work will be to explore, experimentally and theoretically, nonlinear and quantum optical effects in the x-ray spectral regime. These are novel fields of research offering many exciting new opportunities, which now become possible due to the recent and expected improvements in the x-ray sources. It should be emphasized that the physical description of nonlinear and quantum effects in the hard x-ray regime have unique features that are substantially different from those associated with nonlinear and quantum processes commonly observed in the optical regime of the spectrum. Indeed, recently, the number of works associated with nonlinear and quantum effects in the x-ray regime, is growing rapidly. Dr. Sharon Shwartz and his colleagues described a method for generating each of the four Bell states in the x-ray regime. They also described theory and experiment showing x-ray parametric down-conversion in the x-ray region where photo-ionization dominates. As such it is the first experiment that allows measurement of the x-ray non-linearity in this region, and also the first experiment to blend quantum optics with x-ray optics. More recently, Dr. Shwartz together with his colleagues observed second harmonic generation in the x-ray regime. Dr. Shwartz also collaborated with scientists from Stanford, SLAC and Berkeley and demonstrated the mixing of an x-ray light with a visible light, and x-ray nonlinear Compton scattering. These experiments, which use x-ray free electron lasers, push the envelope of extreme nonlinear optics at sub-angstrom wavelengths.The central themes of the programs will be: 1) the study of second harmonic generation in its own right and for application to the measurement of the temporal structure of the x-ray free electron laser 2) Experiments on parametric down conversion from x-ray to visible. 3) More advanced experiments will be aimed at demonstrating extreme non-degenerate quantum optics."