Basic considerations -- X-ray sources -- The INELAX instrument -- Other approaches to inelastic X-ray scattering -- Applications of inelastic X-ray scattering -- The future of the technique -- Final remarks.

Inelastic scattering of X-rays with very high energy resolution has finally become possible thanks to a new generation of high-intensity X-ray sources. This development marks the end to the traditional belief that low energy excitations like lattice vibrations cannot be resolved directly with X-rays: Inelastic scattering experiments allow to observe directly the small energy shifts of the photons. Studies of lattice vibrations, of excitations in molecular crystals, of collective excitations in liquids and electronic excitations in crystals demonstrating the broad applicability and power of this new technology are discussed in this book. The progress in this field opens up fantastic new research areas not only in physics but also in other disciplines such as materials science,biology and chemistry.