"High-order harmonic generation (HHG) as a relatively inexpensive and widely available alternative source in the x-ray region was discovered nearly 20 years ago. The physics is now well understood. Applications are emerging, e.g. in attosecond science. The main difficulty, however, remains the low conversion efficiency and the low number of photons available. Efforts must be undertaken to further increase the output energy of high-order harmonic. The main objective of this proposal is to optimize high order harmonic generation and to explore some of its applications. Single atom response and collective effects will be both considered for the optimization of high-order harmonic generation. The mixing of the fundamental laser with double frequencies and even with an attosecond pulse train will be used to enhance the single atom efficiency. The collective emission will be optimized by increasing the total radiation volume and by achieving phase-matching conditions in different spectral range, developing in particular, quasi-phase matching techniques with weak counter propagating beams. Three applications of intense high-order harmonics will be explored, time-resolved digital in-line holography, nonlinear optics in the extreme ultraviolet range and seeding for free-electron laser research."