This is a presentation of the utilitarian approach to punishment. It is meant for students. A note added in July, 2022 advises the reader about the author's current views on some topics in the paper. The first section discusses Bentham's psychological hedonism. The second briefly criticizes it. The third section explains abstractly how utilitarianism would determine of the right amount of punishment. The fourth section applies the theory to some cases, and brings out how utilitarianism could favor punishments more or (...) less severe than the lex talionis. (shrink)