Anarcho-capitalism (also referred to as free market anarchism, market anarchism, and private-property anarchism) is a libertarian political philosophy that advocates the elimination of the state in favor of individual sovereignty in a free market. In an anarcho-capitalist society, law enforcement, courts, and all other security services would be provided by privately funded competitors rather than through taxation, and money would be privately and competitively provided in an open market. Therefore, personal and economic activities under anarcho-capitalism would be regulated by privately run law rather than through politics.
Various theorists have differing, though similar, legal philosophies which are considered to fall under "anarcho-capitalism." The first well-known version of anarcho-capitalism was formulated by Austrian School economist and libertarian Murray Rothbard in the mid-twentieth century, synthesizing elements from the Austrian School of economics, classical liberalism, and nineteenth century American individualist anarchists Lysander Spooner and Benjamin Tucker (rejecting their labor theory of value and the normative implications they derived from it). In Rothbardian anarcho-capitalism, there would first be the implementation of a mutually agreed-upon libertarian "legal code which would be generally accepted, and which the courts would pledge themselves to follow." This legal code would recognize sovereignty of the individual and the principle of non-aggression.
Read more about Anarcho-capitalism: Internal Debates, Anarcho-capitalism and Other Anarchist Schools, Anarcho-capitalism and Austrian Economics, Criticisms