Spectroscopy is one of the fundamental tool in condensed matter physics, materials science and nanoscience. Resonant spectroscopies, like Resonant Inelastic X-ray Scattering (RIXS) and angle resolved Resonant PhotoEmission Spectroscopy (RPES), offer invaluable information on the system under investigation, being able to probe different types of excitations, from electron-hole pairs (excitons), to spin-flip, to collective excitations, to orbital and magnetic excitations. This proposal aims at improving the present theoretical description of these two powerful spectroscopies, in order to gain a better understanding of moderately correlated systems and, on the long term, to offer a future tool to describe resonant spectra of strongly correlated systems. The proposal relies on the combination of efforts between the candidate (whose experience is mainly in X-ray spectroscopy) and the community working in low energy excitations mainly via many body perturbation theory. Such joint effort is necessary given the difficult task of being able to describe both deep core level excitations and low energy excitations, with finite momentum transfer, which can both give signatures of the many body physics in the system. The project is mainly devoted to the improvement in the description of RIXS, in particular in the extension of the first (ab-initio) attempts done recently by collaborators of the host group to the complicated case of indirect RIXS. On the side, the candidate aims at making her previous work on RPES available to the vast community working in photoemission, creating an interface with a well established and well structured tool widely used for interpreting X-ray results. The impact of the outcomes of such proposal are huge: it will connect theoretical communities working in different energy ranges, and it will represent an invaluable tool for interpreting the huge amount of experimental output on resonant spectrscopies from European synchrotron radiation facilities.