The present proposal outlines a postdoctoral training for Carlos Hernandez-Garcia (Experienced Researcher, ER) for two years in JILA at the University of Colorado in USA (outgoing host institution, OH), followed by a third year at the Universidad de Salamanca (USAL) in Spain (return host institution, RH). The applicant will have the opportunity to strengthen his existing collaboration with the outgoing host, which started in the form of short visits during his PhD studies.The research proposal addresses the novel challenges associated to the emerging field of intense mid-infrared laser-mater interactions. The ER, and the two host institutions, were involved in the first demonstration of efficient coherent X-ray generation from the high-order harmonics (HHG) obtained with table-top mid-infrared source, reported in Science journal in June 2012. This milestone is taken as a starting point in this proposal. The promising future of these new compact X-ray sources will be the stimulus of basic research in this field. First, there is evidence of new phenomena unique for intense-laser interaction in the mid-infrared spectral range, and secondly, it is necessary to obtain characterization schemes for the novel X-ray beams, which requires a proper analysis of the interaction of matter with coherent X-rays, including the special properties of these new sources.During his PhD, the ER has acquired experience in theoretical and experimental work on intense laser-matter interaction. The present proposal involves theoretical as well as experimental training. The proposed training is designed to develop along three different lines: designing a new generation of X-ray sources based on the results of theoretical calculations, performing a theoretical study how matter interacts with these newly designed X-ray beams towards their possible applications, and acquiring theoretical and experimental skills of special interest for the future career development of the ER in the RH.