This entry for the forthcoming The New Palgrave Dictionary of Economics (Second Edition) surveys the economic analysis of public enforcement of law - the use of public agents (inspectors, tax auditors, police, prosecutors) to detect and to sanction violators of legal rules. We first discuss the basic elements of the theory: the probability of imposition of sanctions, the magnitude and form of sanctions (fines, imprisonment), and the rule of liability. We then examine a variety of extensions, including the costs of imposing fines, mistake, marginal deterrence, settlement, self-reporting, repeat offenses, and incapacitation.