In the past fifteen years, neutrino physics has revolutionised our understanding of particle physics. The discovery of neutrino oscillations implies that neutrinos have masses and mix: this is the only particle physics evidence of new physics beyond the Standard Model to date. Their origin remains a major challenge.The NuMass project will focus on new physics at low energy scales, below the one reachable at the LHC. This approach is opposite to widely studied Standard Model extensions, which invoke new physics at scales so high that they will never be tested directly, and orthogonal to TeV models accessible at the LHC. The NuMass idea is that new particles in Nature could be hidden away not because they are too heavy but because, although light, they interact too weakly with ordinary matter. Neutrinos are by far the least understood of the standard fermions: if new particles are indeed at low scales, below the electroweak one, a likely scenario is that they couple more strongly to neutrinos than to other standard particles, e.g. quarks. Therefore, neutrinos are a unique portal into low energy physics.The NuMass project will adopt a unique approach combining particle theory, phenomenology and cosmology. It will propose low energy extensions of the Standard Model and embed them in a consistent theory. It will study their signatures in experiments and their impact in the Early Universe. It will exploit the wide experimental programme, e.g. T2K, MicroBooNE, NOvA, GERDA, which will provide new data in the near future, to constrain the properties of the models.The NuMass ultimate goal is to unveil a new theory of particles and interactions at low energy: its success would be groundbreaking as it would open a completely new perspective on the fundamental laws of Nature. New theoretical challenges would arise to explain why the new sector is light, and new experimental ones to test the new particles and interactions, leading to new directions in particle physics.