"SAGA aims at advancing the mathematical foundations of CAD technology. Based on some exploratory work, we believe that this technology can be greatly enhanced by exploiting results and techniques from many different fields in mathematics: Algebraic Geometry, Symbolic Computation, but also Numerical Analysis and Approximation Theory. The main goal of the proposal is to exploit the diverse knowledge of the partners (from universities, research institutes, and industry) for training a new generation of mathematicians. To master the challenges of combining CAD and Algebraic Geometry, Europe needs new experts with experience from different schools of thought and applications, who have built their own Europe-wide contact net and have either gathered important industrial experience before pursuing an academic career or have academic research experience before entering industry. SAGA offers an environment of researchers from different areas with a common vision, and tailor-made training opportunities to learn geometric modeling both from the industrial and the fundamental mathematics perspective. The network-wide training will offer one large training event per year, i.e. a school, two study groups for joint problem solving, and a final workshop. Complementary skills will be trained both locally and also at the annual events that are open also for external researchers. The topics envisaged for training-through-research include how current CAD algorithms can be improved when several representations for the same object are available, with easily performed conversion between them; how algebraic and geometrical tools can be adapted to solve CAD problems; how concrete CAD challenges (like hole filling, offsets, singularities) can be dealt with using Algebraic Geometry; as well as practical problems posed by industry."