This is the proceedings of the special "Abelian Groups, Rings and Modules Conference" held at Auburn University in September 2004 in honour of Professor Edgar E. Enochs. The volume consists of 25 original research papers and one survey, related to a variety of topics of modern algebra inspired by, or closely related to, the influential research of Enochs over the past decades. Of course, the focus is naturally on module theory over commutative rings. Given the number of interesting contributions in this volume, it is impossible to list them all in a short review. We only mention four of them: a survey on Gorenstein homological algebra written by Enochs and Jenda presenting some of the recent ideas and challenges of this topical area, a paper by Fuchs, Heinzer and Olberding developing commutative ideal theory without finiteness conditions, a paper by Goebel and Shelah characterizing all torsionless linearly compact abelian groups, and a paper by Hassler and Wiegand presenting a method of construction of large indecomposable modules over hypersurface singularities. The book is yet another proof of the lasting impact of Enochs on a number of areas of contemporary module theory. It will definitely be of interest both for researchers and for graduate students in algebra.