Gauge Theories provide the most successful framework for the description of nature, and in particular of high energy physics. However, extracting reliable predictions relevant for experiment from gauge theory has remained a major challenge which so far requires massive use of computer algebra. Over the last decade an entirely new approach to quantum gauge theories has begun to emerge, initiated by a celebrated duality between gauge and string theory. This has brought an area of science into gauge theory that seemed unrelated a few years before, namely the theory of low-dimensional statistical systems and strongly correlated electron systems. The paradigm governing this is to view "Gauge Theory as an Integrable System". The partners of this network represent different communities from gauge theory, statistical physics and computer algebra. With the proposed Initial Training Network we will carry the emerging multidisciplinary interaction to an entirely new level, bridging the gaps between our research fields in the context of graduate training activity. We believe that coordinated education of young scientists in all the tools under development from the different communities offers tremendous potential to make progress in the understanding and application of gauge theory. A group of carefully selected private sector partners will assist dissemination of results, methods and ideas into neighboring scientific disciplines as well as to the general public. At the same time, they will also be vital in preparing the early stage researchers for active and leading roles in academia and beyond.