This is the first English translation of Durkheim's lecture for the first class of the fourth and final year of his course ‘On the General Physics of Law and Morality’. The content from the previous year's course is contained in Professional Ethics and Civic Morals (Durkheim  1992). Durkheim discusses the importance of a special theory of sanctions and provides a typology of their negative and positive forms. He makes a case for the sociology of penalties and responsibilities, one based on the examination of their external and visible characteristics. Crucially, Durkheim displaces the ostensible causal importance of the intentions of juridical subjects, whether legislators or wrong-doers. The translation is accompanied by an extended critical introduction by R. P. Datta and Fr. Pizarro Noël.