This is the preface and opening chapter of a forthcoming book on Oxford University Press about the way that geography shapes legal rules and understandings - and how fundamental changes in American power and in world politics have challenged and sometimes altered the traditionally territorial system of legal jurisdiction. Do the laws of the United States stop at the water's edge? If not, do they operate differently beyond American territory? These questions often arise today with regard to hot-button issues such as the future of Guantanamo. But they have a long and fascinating history, dating back to the American Revolution and encompassing episodes as varied as the military occupation of parts of Mexico, the U.S. District Court for China, American empire after the Spanish-American War, extraterritorial regulation, and postwar Status of Forces Agreements. This book explores changes in territoriality and extraterritoriality through these episodes, covering questions of both constitutional and statutory law, world and domestic politics, and internal and external borders. Two main arguments are advanced. First, instances of extraterritoriality, while varied, share a common ground in their focus on managing and minimizing legal difference, differences that are a direct result of the territorial basis of sovereign rule, which has been the organizing principle of the international system for centuries. Second, American law has long employed what I call intraterritoriality as a way to facilitate the power of the United States. The United States comprises a complicated mix of territory. Within the states constitutional rights apply fully, but throughout much of American history only a limited set of rights have applied in other U.S. territories. Intraterritoriality is in a sense a mirror of extraterritoriality. Extraterritoriality generally serves to mitigate difference, whereas intraterritoriality generally serves to establish difference. Throughout the book I contend that we cannot understand the evolution of extraterritoriality and intraterritoriality in U.S. law without understanding the broader international context. American notions and doctrines of territoriality were themselves drawn from international law. Yet these notions and doctrines evolved over time to reflect American national interests. As the United States grew from a weak state to a global superpower, and as the nature of world politics itself changed, principles of both extraterritoriality and intraterritoriality have been transformed.