Anarcho-capitalism, (also market, private property, or liberal anarchism) is a specific form of libertarianism which satisfies two conditions:
1. The absence of involuntary government.
2. A neo-Lockian property system prevails.
The first condition is the definition of anarchism. Anarcho-capitalism is a particular type of anarchism. However, anarchist schools of thought have different conceptions of property. Extreme anti-propertarian schools deny the validity of private property altogether, preferring some collectivist or corporate property system. Others accept most neo-Lockean property conventions, but differ in some significant way. E.g. Geo-anarchists view only man-produced items as property, and hold land and natural resources to be commons.
Neo-Lockean or "sticky" property is the convention/system in which all scarce resources are either unclaimed (and available for homesteading) or private property, and that such property remains the property of the owner until a consensual exchange occurs. The single exception is an abandonment condition, which allows abandoned property to return to unclaimed/homesteadable status.
Anarcho-capitalism can be seen as a system where all goods and services are provided by the market. In particular, anarcho-capitalists contend that the service of defending individual rights should be done by firms, mutuals, coops, neighborhood groups, or some other voluntary means, rather than a compulsory State monopoly. The State by definition has an effective monopoly on the legal use of violence in a particular geographic area. In an anarcho-capitalist system, courts and police are services on the market. The most common prediction of how such a market might look consists of competing PDAs (Private Defense Agencies) whose services are bought on an insurance basis. Another model envisions leasehold arrangements.
 History and Literature
Gustave de Molinari was the first to explicitly advocate doing away with the State's monopoly on defense of rights in Production of Security (1849.) However, most consider Murray Rothbard to be the father of anarcho-capitalism. He coined the term in the early 1960s, melding the American individualist anarchism of Lysander Spooner and Benjamin Tucker with the neo-classical (Austrian school) economics of Ludwig von Mises, and the property theory of John Locke and the classical liberals.
Liberalism has always had an anti-statist strain. John Locke asserted a right of revolution. William Godwin and Edmund Burke wrote anarchist tracts. Henry David Thoreau wrote that "government is best which governs not at all." Herbert Spencer asserted a "right to ignore the State," and his protege Auberon Herbert developed voluntaryism, his term for private property market anarchism.
"Man, Economy, and State," "Power and Market," "The Libertarian Manifesto," and "The Ethics of Liberty" are Rothbard books in the anarcho-capitalist canon. Other important works are "The Market for Liberty" by Linda and Morris Tannehill, which explains how non-territorial PDAs could work on an insurance basis, and "The Machinery of Freedom" by David Friedman. While Rothbard bases anarcho-capitalism on natural rights and non-aggression, Friedman takes more utilitarian approach. Friedman believes that anarcho-capitalism would have a bias toward libertarian values, but would not guarantee that result. Walter Block and Hans Hermann Hoppe are also anarcho-capitalist luminaries.
Agorism is a branch of anarcho-capitalism which stresses a transition strategy of counter-economics, i.e. participation in the untaxed counter-economy, aka the black market. Another strategy is becoming PT (perpetual tourist), which involves living in a country outside the State that tries to impose taxes, and keeping your money in a third country, making it extremely difficult be extorted from. But most anarcho-capitalists do not resort to such radical strategies, rely on
- educating the public about the efficacy of voluntary society vs. the inefficiency and immorality of government aggression
- creating parallel structures, i.e. voluntary alternatives to services currently provided by State: neighborhood arbitration, alternate currencies.
- protecting rights, such as opposing drug prohibition, gun control, and supporting freedom of speech, financial and personal privacy (EFF
- addressing injustices, such as ), victimless "crimes," police brutality
- anti-war activism, since war is the most murderous act of State, and tends to increase its power.
Another strategy is "Left Libertarianism." Left libertarians embrace the popular Marxian definition of "capitalism" as the collusion of capitalists and State to exploit the workers. Some use the term "free market anti-capitalism." Left libertarians are concerned with issues typically considered "left," and include mutualists and geoists, which are similar to anarcho-capitalism in many ways.
 Objections to anarcho-capitalism
Many objections to anarcho-capitalism are rebutted fairly easily by simply comparing or contrasting it with the State. Critics often try to get away with comparing anarcho-capitalism to utopia rather than the relevant alternative, the State. For example, arguing that "anarcho-capitalism would lead to one big organization taking power over everyone else" loses its force when we see that the state is already such an organization. At worst, we get a period of liberty before the state reemerged. But there are reasons why anarcho-capitalist societies would be more peaceful than States, which have a proven record of democide and war. With non-territorial PDAs, weapons of mass destruction are generally unusable, since killing your customers is bad business. And while State fund their martial expenses by plunder (taxation), PDAs must satisfy customers to get paid. Warlike and renegade PDA would be more expensive, in both weaponry and wages paid, so they are at a competitive disadvantage. Shootouts lose customers. PDAs that deal with each other often would likely have preselected arbiters.