‘Odds, evens, and shells’ considers the fundamental property laws governing nuclear structure. It explains element stability and abundance, as well as the quantum rules, magic numbers, shells, and binding energy that explain atomic and element structure. An effective guide to stability, and the pattern of radioactive decays, is given by the semi-empirical mass formula. As nature seeks stability by minimising energy, a nucleus seeks to lower the total mass or increase the binding energy by emitting an alpha particle cluster, by beta decay, or by splitting in two, as in uranium fission. Alpha decay and technetium, the lightest element that is totally radioactive, and thus without any stable isotopes, are also described.