The project aims to facilitate the collaborative research towards theory, design, manufacture and experimental tests of high-quality periodically bent crystalline structures as well as theoretical and experimental studies of the radiation formed in crystalline undulators.The idea of the crystalline undulator is based on the channeling phenomenon. Its advantage is in extremely strong electrostatic fields inside a crystal which are able to steer the particles much more effectively than even the most advanced superconductive magnets. A crystal with periodically bent crystallographic planes or axes can force particles to move along nearly sinusoidal trajectories and radiate electromagnetic waves in hard X ray and gamma ray frequency range.This opens the prospect of creation of novel light sources that will find their application in technology, medicine and basic sciences: nuclear, solid state and plasma physics, molecular biology, etc.It is planed to combine within a common project utilization of state-of-the-art technologies: molecular beam epitaxy, laser ablation, low pressure chemical vapour deposition, low energy plasma enhanced chemical vapour deposition with advances theoretical methods aimed to quantitative understanding of the underlying physical processes which will allow to manufacture bent crystals with preassigned shape of channels. The quality of the manufactured crystals will be controlled by several advanced methods: X-ray diffraction studies, transmission electron microscopy, atomic force microscopy, scanning electron microscopy and optical profilometry.Accelerator test of the crystalline undulators will be complemented with extensive Monte-Carlo simulations of particle channeling and emission of the radiation.