Topological phenomena in solid state physics is currently a hot topic which attracts active interest worldwide due to its fundamental aspects and possible applications e.g. in quantum computation. In this talk, an overview will be given of the planned research directions and currently obtained results in newly established laboratory at Moscow Institue of Physics and Technology in the field of topological phenomena in superconducting hybrid structures. This research is supported by the megagrant 14Y26.31.0007 in 2014-2016.