For the first time in history, completely solving an interacting four-dimensional quantum gauge theory appears to be within reach, thanks to the gauge-string duality and the integrable structures discovered in planar maximally supersymmetric Yang--Mills theory and its string dual. Pursuing this overall goal, the present proposal aims at studying two important types of quantities in these theories: Structure constants and scattering amplitudes. The outgoing phase is to be carried out at the Institute for Advanced Study in Princeton under the supervision of Prof. Juan Maldacena, the discoverer of the gauge-string duality and a world-leading figure in the identification and application of the integrable structures appearing in this context. The project will be completed at the DESY Hamburg theory group, where the applicant will be supervised by Prof. Volker Schomerus. The successful completion of the project will contribute significantly towards understanding the gauge-string duality, as well as the general structure of gauge theory scattering amplitudes. The excellent scientific and complementary training provided during the execution of the project will have a strong impact on the career prospects of the researcher, whose goal is to establish himself permanently at a leading European research institution.