Libertarianism is an umbrella political ideology that encompasses theories from the left and right spectrum. Examples of right-libertarianism are anarcho-capitalism and Chicago schoolers. An example of left-libertarianism is libertarian socialism.
Deviating from right-libertarianism, left-libertarians hold that mixing one's labor with natural resources or claiming them is not enough to create property rights . This follows to natural resources should either be distributed in an egalitarian manner either through collective ownership or lack of ownership. This ideology is also notably anti-authoritarian.
Libertarian socialism attempts to create a non-bureaucratic and non-hierarchical society where the means of production are not owned privately, while still retaining personal property  This is an umbrella that encompasses anarcho-communism, anarcho-syndicalism, and libertarian Marxism to name a few.
Right libertarians are often adherents to the Non-aggression principle (NAP). In which you may only use force if someone has previously acted forcefully against you. Some flavors of libertarianism view the NAP as the basis for all normative ethical action. This has been criticized as a poor grounding of ethics, even if it is correct . Importantly, it can be hard to identify the aggressor in situations invoking NAP . A common phrase among right-libertarians is "taxation is theft" .
Anarcho-capitalism draws its philosophical grounding from Murrary Rothbard and praxeology . Asserting that humans engage in purposeful behavior is somehow able to deduce proper economic action inside a society. It fundamentally rejects empiricism as a useful tool in understanding economic and social relations, instead opting for verbal analysis. It promotes complete free market capitalism and complete removal of the state. Instead of publicly funded courts, police, and other services traditionally provided by the state, An-caps want everything completely privatized. This market will apparently be the fairest to the consumer because of competition between opposing private institutions.
Objectivism is a "philosophy" that originates from novelist Ayn Rand. Objectivism grounds ethical action in rational-self interest. In metaphysics it borrows from Aristotle insofar that A is A. An object is separate from human and is not subjective. It's too bad for Ayn Rand though, because these objects would be intrinsic, meaning they essentially exist, not objective. It is upon these flawed premises that all of objectivism is based.
Essentially the objectivist is arguing from an epistemological standpoint that if you cannot offer a precise definition for something, you are full of it . This runs into Wittgenstein's Meaning As Use and other linguistic analysis, which Ayn Rand never actually answers .
Ayn Rand rejected the label of libertarianism, arguing that they were hippie anarchists and enemies of freedom . The reason Objectivism is labeled as a libertarian philosophy, despite Rand's eschewing of the label, is because its positions politically line up completely with stock libertarianism.
Minarchism is slightly to the left of anarcho-capitalism. Minarchists hold that the only validity of a state is protecting individuals from aggression, theft, contract breaches, and fraud. The state accomplishes this through courts, police, and the military. According to some Minarchists, the state also operates fire departments, prisons, and legislative bodies to accomplish the aforementioned goals  . Minarchists hold that the state ought not to use its monopoly on force to interfere with voluntary transactions between individuals. It logically follows for most minarchists that the freest possible market capitalism is the only system that will produce economic prosperity.
Modern Minarhcist philosophers include Robert Nozick, who set himself in opposition to John Rawls. As opposed to Rawls, who argued that distribution of social goods should be based from an original position as to not disadvantage anyone in society, Nozick argues that distribution of goods is only just if the people engaging in free exchange originated from a just starting position. Nozick is also an adherent to the NAP, which is not necessarily true of all minarchists.
Most controversially about Nozick was that he viewed the NAP as allowing non-coercive and consensual enslavement contracts between adults. Nozick rejects the concept of inalienable rights . The objection often offered to Nozick is that slavery can in no way be non-coercive.
- Carlson, Jennifer D. (2012). "Libertarianism". In Miller, Wilbur R. The social history of crime and punishment in America. London: Sage Publications. p. 1007. ISBN 1412988764. "[Left-libertarians] disagree with right-libertarians with respect to property rights, arguing instead that individuals have no inherent right to natural resources. Namely, these resources must be treated as collective property that is made available on an egalitarian basis."
- Berkman, Alexander (1929). Now and After: What Is Communist Anarchism?. "The revolution abolishes private ownership of the means of production and distribution, and with it goes capitalistic business. Personal possession remains only in the things you use. Thus, your watch is your own, but the watch factory belongs to the people."