Mathematics underpins all of modern science and technology but advances in mathematical research are not always applied to maximum advantage in industry. The objective of this Action is to create a Europe-wide partnership to promote collaboration in, and the benefits of, industrial mathematics. The Action will run industry workshops, training weeks, and short-term scientific missions to both academic and industrial hosts, with the general aim of increasing the interaction between industry and academia. Exploiting the mathematical knowledge and methodologies of academics will provide European industry with a competitive advantage. Universities will benefit, as mathematicians are able to focus on practically relevant and cutting edge research problems. The training of Early-Career Investigators in particular will lead to a new generation with problem solving and communication skills and collaborative links that will be essential to maintain the goals of this Action in the future long after this funding has finished.