A system that utilizes negative rights to their logical conclusion, as socialism is to positive rights. The system has an absolutely free Laissez-Faire Capitalist economy, without welfare and without corporatism. It lacks a government as Anarcho-Capitalists (Ancaps) regard it as "an infringement on (negative) rights."
It was created (or at least popularized) by heterodox economist Murray Rothbard. Like regular anarchism, its creator abandoned it for more conservative thought. In the case of Proudhon (the founder of Anarchism), Rothbard created Paleolibertarianism.
Anarcho-Capitalism is an extreme form of modern Libertarianism due to its lack of government in the name of individual liberty. Many Ancaps disagree about issues, such as the rights of gays and copyright.
Many modern Ancaps are peaceful, with the exception of the ones who follow Hans Hermann Hoppe. The supporters of Hoppe (Hoppeans) supported Hoppe's idea that some rights needed to be restricted to preserve Libertarianism and communists needed to be physically removed, while regular Ancaps feel that communists have the rights of people and some even go so far as to say that Communists should be allowed to form communes utilizing private property.