This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters. The theory of modules over groups has its own specific character that plays an imperative role here and, for example, allows a significant generalization of the classical Maschke Theorem on some classes of infinite groups. Conversely, it leads to establishing direct decompositions of artinian modules related to important natural formations, which, in turn, find very efficient applications in infinite groups.