The works of Maria Sklodowska-Curie and Pierre Curie, of their few predecessors and of their many followers addressed over the years the studies of the atomic nuclei - the smallest objects in the Universe which are unique in that they are governed simultaneously by the strong, electromagnetic and weak interactions. In this article we focus on the concept and nature of symmetries, their omni-presence in physics and their impact on the behaviour of the physical systems. Beginning with a short historical overview covering quickly the birth of certain concepts in the ancient times and their evolution until the most modern ones we cover, on an introductory level, the question of space-time symmetries, the connection between the intrinsic degrees of freedom and the spatial behaviour of quantum particles as well as the question of symmetry-induced conservation-laws. We discuss shortly examples of continuous and discrete symmetry groups, the constraints imposed on the energy spectra (degeneracy of levels) by the symmetries of the underlying Hamiltonians, to end with the question of transitions and symmetry imposed selection rules. The article terminates with a short discussion of the symmetry breaking phenomena, spontaneous symmetry breaking and phase-transition induced symmetry-changes.