Abstract: This article discusses the theory of the 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 present the basic elements of the theory, focusing on the probability of imposition of sanctions, the magnitude and form of sanctions, and the rule of liability. We then examine a variety of extensions of the central theory, including accidental harms, costs of imposing fines, mistake, marginal deterrence, settlement, self-reporting, repeat offenses, and incapacitation. Applications to criminal law, the control of driving, environmental enforcement, and tax evasion are included.