Libertarians consider that there is an extended domain of individual freedom
defined by every individual's person and private property, and that no one, whether private citizen or government, may under any circumstances violate this boundary.
Indeed, libertarians consider that no organization, including government, can have any right except those that are voluntarily delegated to it by its members -- which implies that these members must have had these rights to delegate them to begin with.
Thus, according to libertarians, taxation and regulation are at best necessary evils, and where unnecessary are simply evil. Government spending and regulations should be reduced insofar as they replace voluntary private spending with involuntary public spending, and replace private morality with public coercion. To many libertarians, governments should not establish schools, regulate industry, commerce or agriculture, or run social welfare programs. Nor should government restrict sexual practices, gambling, drug usage, or any other 'victimless' crimes. Libertarians also believe in an extremely broad (and in some cases all-inclusive) interpretation of free speech which should not be restricted by government. For libertarians, government's main imperative should be Laissez-faire -- "Hands off!" -- except to protect individual rights.
This idea directly opposes theories such as the Social Contract, which hold that governments are established in order to provide for the welfare and common good of their citizens. Libertarians believe in minimizing the responsibilities of citizens towards the government, which directly results in minimizing the responsibilities of the government towards its citizens.
See Albert Jay Nock's Our Enemy the State for early modern anti-state thought and Lysander Spooner's The Constitution of No Authority for a critique of social contract theory.
Anarchists and minarchists
All libertarians agree that government should be limited to what is strictly necessary, no more, no less. But there is no consensus among them about how much government is necessary. Hence, libertarians are further divided between the minarchists and the anarcho-capitalists, which are discussed at length in specific articles. Both minarchists and anarcho-capitalists differ in their beliefs from the anarcho-syndicalists, anarcho-socialists and libertarian socialists, who are usually considered not to be libertarians at all (the feeling is mutual; anarcho-socialists and libertarian socialists claim that capitalism is incompatible with freedom, and thus libertarian/anarcho-capitalists cannot be considered libertarians at all). The Vosem Chart places anarcho-syndicalists in a separate slot from libertarians.
The minarchists believe that a "minimal" or a "night-watchman" state is necessary to guarantee property rights and civil liberties, and is to be used for that purpose only. For them, the proper functions of government might include the maintenance of the courts, the police, the military, and perhaps a few other vital functions (e.g., roads). While they are technically statists since they support the existence of a government, they would resent the connotations usually attached to this term.
The anarcho-capitalists, believe that even in matters of justice and protection and particularly in such matters, action by competing private responsible individuals (freely organized in businesses, cooperatives, or organizations of their choice) is much better than action by governments. While they consider themselves to be anarchists, they insist in rejecting the connotations often attached to this term regarding support of a socialist ideal.
Minarchists consider that they are realists, while anarcho-capitalists are utopian to believe that governments can be wholly done without. Anarcho-capitalists consider that they are realists, and that minarchists are utopian to believe that a state monopoly of violence can be contained within any reasonable limits. Critics of both these positions generally point to the historical record of democratic governments as evidence that democracy and popular rule have succeeded not only in containing government abuse of freedom, but have in fact transformed the state from a violent master of the people into their loyal and peaceful servant.
The minarchist/anarcho-capitalist division is very friendly, and not the source of any deep enmity, despite the sometimes involved theoretic arguments. Libertarians feel much more strongly about their common defense of individual liberty, responsibility and property, than about their possible minarchist vs. anarchist differences. Since both minarchists and anarchists believe that existing governments are far, far too intrusive, the two factions seek change in almost exactly the same directions.
Many libertarians don't take a position with regard to this division, and don't care about it. Indeed, many libertarians consider that governments exist and will exist in the foreseeable future, up to the end of their lives, so that their efforts are better spent fighting, containing and avoiding the action of governments than trying to figure out what life could or couldn't be like without them. In recent years libertarianism has attracted many "fellow-travelers" (to borrow a phrase from the Communists) who care little about such theoretical issues and merely wish to reduce the size, corruption, and intrusiveness of government.
Some libertarian philosophers argue that, properly understood, minarchism and anarcho-capitalism are not in contradiction. See Revisiting Anarchism and Government by Tibor R. Machan.
Utilitarianism, natural law, and reason
Libertarians tend to take either one of an axiomatic natural law point of view, or a utilitarian point of view, in justifying their beliefs. Some of them (like Frederic Bastiat), claim a natural harmony between these two points of view (that would indeed be but different points of view on a same truth), and consider it irrelevant to try to establish one as truer.
An exposition of utilitarian libertarianism appears in David Friedman's book The Machinery of Freedom, which includes a chapter describing an allegedly highly libertarian culture that existed in Iceland around 800 AD.
For natural rights libertarianism, see for instance Robert Nozick.
See also relevant paragraphs about this difference in points of view in the article about Anarcho-capitalism.
An alternate justification for libertarian ideas (broadly speaking), predicated on the use of reason and the observance of a certain code of ethics (rather than social ends) is contained within the philosophy of Objectivism established by Ayn Rand.
Some libertarians do not attempt to justify their beliefs in any external sense; they support libertarianism because they desire the maximum degree of liberty possible within their own lives, and see libertarianism as the most effective political philosophy towards this end.
Controversies among libertarians
Libertarians do not agree on every topic. Although they share a common tradition of thinkers from centuries past to contemporary times, no thinker is considered a common authority whose opinions are to be blindly accepted. Rather, they are generally considered a reference with which to compare one's opinions and arguments.
These controversies are addressed in separate articles:
Contemporary American libertarians