The properties of the lowest excited states of atomic nuclei offer a very sensitive test for nuclear structure theories. To identify and distinguish the shape phase transitions, one needs the variation behaviors of the energy ratios with respect to the neutron or proton number of the nuclei. The possibility of generating images of the variation behaviors of energy levels and energy ratios by exploiting the large body of data on stable and near-stable nuclei, whose accumulation over the past decades now permits, prompted us to produce this atlas which illustrates in a simple and effective way these behaviors. The atlas represents the experimental data of the energy levels and energy ratios of the 2_1^+, 4_1^+, 2_2^+ and 4_2^+ states of 645 even-even nuclei. The interpolation surfaces of the values of energy levels and energy ratios, E(2,1+), E(2,2+), E(4,1+), E(4,2+), E(4,1+)/E(2,1+), E(4,2+)/E(2,2+), E(2,2+)/E(2,1+), E(4,2+)/E(4,1+), E(4,2+)/E(2,1+) and E(4,1+)/E(2,2+), through all points of the even-even nuclear landscape are presented. The variation of these values with respect to each chain of isotopes and isotones are displayed using two-dimensional figures. Visualization of the data through visual imagery has been considered an effective way for connecting abstract and concrete ideas as well as allowing the emergence of the significant patterns. Moreover, we will see that it is possible, in many if not most cases, to understand the detailed results of complex calculations of the nuclear structure theories with an absolute minimum of formalism and often by inspection. The introduction of this atlas contains a brief account of some topics of present-day interest in theoretical nuclear structure. These topics can be used to explain the existence of a few typical patterns of nuclear spectra as well as some of the systematic changes in these patterns over sequences of nuclei. Researchers working on nuclear theory will ο¬nd this atlas handy to understand the nuclear structure theories
