This is the proceedings of the conference on "Groups, Rings, and Group Rings" held at Ubatuba, Brazil in July 2004 in honour of Professor Polcino Milies. The volume consists of 29 original research papers and four surveys, written by some of the leading experts on group-ring theoretic methods of (non-commutative) group theory. Further topics include Lie and Jordan (super) algebras and applications to coding theory. The book presents a variety of tools and results of the contemporary theory of group rings. It will be of considerable interest for researchers as well as graduate students in this active branch of modern algebra.