The AMORNET Network aims at training a world-class cohort of doctoral researchers (DRs) who will invent and implement the next generation of mathematical algorithms solving geometric problems arising in robotics. We aim to build strong lasting links between strategically selected industry and academic partners, combining a wide range of mathematical expertise with advanced expertise on robotics design and geometry. The research programme targets, in particular, computational problems arising from soft robotics, a topical area where robotics manipulators are no more rigid but designed with flexible bodies. Soft robots are expected to be more secure when interacting with their environment and to enjoy more mobility properties. Hence, robotics applications of soft robots are numerous and appealing but, to let the Industry adopt them, there is an urgent need to sharpen their geometric designs, models, and identify their mobility properties. This gives rise to challenging and stimulating problems in computational mathematics, especially since these are non-linear but algebraic. The planned training network will provide research and training opportunities to a new generation of DRs, who, in the long-run, shall address the Grand Challenge of making computational mathematics efficient and accurate enough to solve these algebraic problems arising in robotics. This will enable the design of robotics manipulators which will be safer, more reliable and more efficient. The AMORNET Network involves a number of industrial partners and academic facilities that will be used to validate experimentally the theoretical achievements brought by the DRs. The AMORNET Network will deliver more efficient and accurate mathematical methods, algorithms for solving algebraic problems, and their particular applications to issues robotics combined with experimental validation will accelerate the adoption of soft robotics by the EU Industry.