Anarchy is a form of society without rulers. As a type of stateless society, it is commonly contrasted with states, which are centralized polities that claim a monopoly on violence over a permanent territory. Beyond a lack of government, it can more precisely refer to societies that lack any form of authority or hierarchy. While viewed positively by anarchists, the primary advocates of anarchy, it is viewed negatively by advocates of statism, who see it in terms of social disorder.

The word "anarchy" was first defined by Ancient Greek philosophy, which understood it to be a corrupted form of direct democracy, where a majority of people exclusively pursue their own interests. This use of the word made its way into Latin during the Middle Ages, before the concepts of anarchy and democracy were disconnected from each other in the wake of the Atlantic Revolutions. During the Age of Enlightenment, philosophers began to look at anarchy in terms of the "state of nature", a thought experiment used to justify various forms of hierarchical government. By the late 18th century, some philosophers began to speak in defence of anarchy, seeing it as a preferable alternative to existing forms of tyranny. This lay the foundations for the development of anarchism, which advocates for the creation of anarchy through decentralisation and federalism.

As a concept, anarchy is commonly defined by what it excludes. Etymologically, anarchy is derived from the Greek: αναρχία, romanized: anarchia; where "αν" ("an") means "without" and "αρχία" ("archia") means "ruler". Therefore, anarchy is fundamentally defined by the absence of rulers.

While anarchy specifically represents a society without rulers, it can more generally refer to a stateless society, or a society without government. Anarchy is thus defined in direct contrast to the State, an institution that claims a monopoly on violence over a given territory. Anarchists such as Errico Malatesta have also defined anarchy more precisely as a society without authority, or hierarchy.

Anarchy is often defined synonymously as chaos or social disorder, reflecting the state of nature as depicted by Thomas Hobbes. By this definition, anarchy represents not only an absence of government but also an absence of governance. This connection of anarchy with chaos usually assumes that, without government, no means of governance exist and thus that disorder is an unavoidable outcome of anarchy. Sociologist Francis Dupuis-Déri has described chaos as a "degenerate form of anarchy", in which there is an absence, not just of rulers, but of any kind of political organization. He contrasts the "rule of all" under anarchy with the "rule of none" under chaos.

Since its conception, anarchy has been used in both a positive and negative sense, respectively describing a free society without coercion or a state of chaos.

When the word "anarchy" (Greek: αναρχία, romanized: anarchia) was first defined in ancient Greece, it initially had both a positive and negative connotation, respectively referring to spontaneous order or chaos without rulers. The latter definition was taken by the philosopher Plato, who criticised Athenian democracy as "anarchical", and his disciple Aristotle, who questioned how to prevent democracy from descending into anarchy. Ancient Greek philosophy initially understood anarchy to be a corrupted form of direct democracy, although it later came to be conceived of as its own form of political regime, distinct from any kind of democracy. According to the traditional conception of political regimes, anarchy results when authority is derived from a majority of people who pursue their own interests.

During the Middle Ages, the word "anarchia" came into use in Latin, in order to describe the eternal existence of the Christian God. It later came to reconstitute its original political definition, describing a society without government.