We want to establish a new generation of theoretical studies from which information on the structure of strongly interacting particles (hadrons) will emerge. Key elements will be computations of new high-order terms in QCD perturbation theory and of higher twist corrections, both of which are crucial for the precision analysis of processes with large momentum transfer. These theoretical calculations will go hand in hand with state-of-the-art phenomenological studies. A central theme of our proposal is to improve and strengthen the theoretical foundations for the science program at the future electron-ion collider (EIC), especially for its planned efforts to obtain three-dimensional "tomographic" images of protons and nuclei. Our proposed research is highly relevant not only for the EIC, but for strong-interaction physics all the way from fixed-target facilities to the LHC.