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The fields of X-Ray Spectroscopy in Atomic and Solid State Physics have undergone spectacular growth, sometimes rather anarchic, during the past decade. The old mold of X-ray spectroscopy has been burst, and this ASI provided an in-depth exploration of theory and recently developed techniques; however, some work still needs to be done to create a new frame and reduce anarchy in the field. The purpose of this Institute was to gather atomic and solid state physicists working in theoretical and new experimental techniques recently developed. The lectures were concerned with, among others, the following fields: theory of X-ray near-edge structure, XPS and AES with conventional and synchrotron radiation sources, PIXE, EXAFS, SEXAFS, XRF, SXS, and molecular spectroscopy. The Institute considered in detail some of these experimental tech- niques and the pertinent theoretical interpretations by selecting an important list of lectures which summarize the scientific contents of the ASI. The truly international character of this NATO ASI, its size, and the high quality of the lecturers contributed to make this school a very fruitful scientific meeting. Two to four general lectures were given each working day and three afternoons were reserved for presentation of current work in the form of posters. We think that these poster presentations reflect the current research work of the participants.