This lengthy chapter deals with modules over rings. Early on, notions like exactness, projectivity, injectivity and flatness of modules are discussed, also through diagram chasing. Duals and tensor products are considered before attention is drawn towards modules over principal ideal domains. This leads to Smith normal form, and generalized Jordan blocks, as well as the Jordan-Chevalley decomposition. Semisimple modules are analyzed, including rings considered as modules over themselves. The concept of density is important here. Then noetherian and artinian modules are studied. The study of nilpotence leads to the Jacobson and Wedderburn radicals, which are studied extensively in the latter part of the chapter. It concludes with a thorough study of units in rings, and of division rings.