What Our current view of the microscopic world is a tremendous success. For the first time in almost a century, we are in the situation when all the particles, needed to explain the results of previous accelerator experiments had been found. In a daring endeavour, the laws of microphysics were applied to the "Universe as a whole" and together with Einstein's General Relativity led to the creation of modern cosmology. As a result, we can describe in details how complex structures of the observed Universe have grown from a simple initial state - a hot and almost homogeneous "soup" of elementary particles. One of the striking things we learned is that the Universe at its largest imaginable scales may be the best place to learn about new particles, complimentary to our accelerators. Why This success of the modern fundamental physics, however, came with a "grain of salt": while the composition of the Universe is measured with high precision, we do not know what particles are behind major cosmic constituents. This paradoxical situation calls for resolution. There are several competing approaches that predict different kinds of particles and, correspondingly, different means of searching for them. These hypothetical particles can either be (i) heavier than the reach of our accelerators or (ii) interacting too weakly with our detectors. The main challenge for fundamental physics is to deduce the properties of these particles and to design experiments to detect them in labs. This is a necessary next step on the road of making a fundamental theory of the Universe How This proposal explores the possibility that hypothetical particles can be lighter than the Higgs boson but have evaded their detection because they interact too feebly with known particles. In such a case, a new type of experiments should be devised to detect new particles, measure their properties and to connect them with observable phenomena in the Universe. One such experiment - Search for Hidden Particles (SHiP) - is currently being designed in CERN. The project will provide theoretical input needed to maximise the scientific return of this and similar experiments planned in other particle physics laboratories around the world. SSR This is a curiosity-driven research project addressing fundamental problems of physics: reconstructing a complete theory of Nature from the body of available data. As with most fundamental research, it promises no guaranteed technological or economical returns in the short run (on the scale of 5-10 years). It is impossible, however, to anticipate its long-term effects (in the same way as it was impossible to imagine in 1900 modern computers and other electronic devices, or to anticipate in 1916 that without corrections due to Einstein's general relativity, the GPS system today would be useless). The proposal does address cultural and societal needs through knowledge dissemination and increasing awareness and interest of the society to the fundamental sciences.