It really depends on what you mean by
Libertarianism, and how you view politics in general. Many of us in the western world view libertarianism as a set of political beliefs between, or otherwise set apart from, the traditional left-right/liberal-conservative dichotomy, but I'd argue against this interpretation, as these terms don't mean quite what they used to. For example, almost everyone in the USA is a liberal, regardless if they identify as a liberal, conservative, or libertarian, which is why the rest of the world calls US conservatives "neo-liberals." To understand this shift, we have to take a look at the history of political philosophy.
Libertarianism is derived from Liberalism, so I think it's important to review the latter in proper historical context. Remember that the political atmosphere of Western Europe before and during the Enlightenment was largely dominated by monarchic empires heavily influenced by the Catholic church. At the same time, merchants had become rather wealthy and powerful, straining the rigid Three Estates hierarchy that dominated "the Middles Ages." Our terms
left and
right actually come from the bicameral French National Assembly, in which Liberals sat on the left and conservatives--those who wished to
conserve the absolute power of the monarchy, the institutionalized privilege of the clergy, and the feudal system of property--on the right. This is why I agree with Quintin Hogg's claim that "[c]onservatism is not so much a philosophy as an attitude": there aren't any concrete tenets, but rather a general desire to conserve current traditions or return to those of the past. Liberals, on the other hand, wanted to limit the powers of government and the church (usually by way of secular, democratic republics), and argued for private property based on the labor theory of property. Many liberal philosophers derived these values from their theological dispositions, arguing that God (the Christian God) had created a state of nature in which humans had natural rights and were given the Earth's resources to use as they pleased.
So if that's Liberalism, what's Libertarianism? Well, the term
libertarian was first introduced as the metaphysical concept that an individual is in control of his or her choices (i.e. that people have free will). When this term entered the political scene, it referred to anarchism ("without rulers"), and these terms were rough synonyms for about 100 years. Libertarians were quite allied with liberals due to their common struggle against absolute rule (Frederic Bastiat, a prominent liberal, sat on the same side with Pierre-Joseph Proudhon, the first self-identified anarchist), but essentially took the Liberal tenets to the extreme: instead of limiting government and church power, they wanted to eradicate them; and instead of private property, they sought something they believed more egalitarian, viz. socialism.
As can be seen in the link Humes fork provided, Libertarianism can roughly be divided into left and right factions, and they differ on how they treat unowned resources. The traditional Libertarianism (i.e. anarchism) is associated with the left, whereas right-libertarianism consists of what most USians call libertarianism (sans modifier), as well as Objectivism and anarcho-capitalism. Essentially, the difference is that right-libertarians are capitalists and left-libertarians, socialists (who range from syndicalists and communists, to the more pro-property mutualists, Georgists, and Tuckerite socialists). Most of the disagreement here comes from how one interprets the Lockean proviso given in the labor theory of property. In Locke's
Second Treatise of Government, he explains that one can only justly appropriate unowned, natural resources if he or she leaves "as much and as good" for others. Right-libertarians believe capitalism embodies this goal; whereas left-libertarians view private property as a violation thereof.
Here, I've pretty well painted Objectivism as a libertarian ideology, but this isn't quite accurate. It is better viewed as Humes fork stated:
Libertarianism is a political ideology only. Objectivism includes libertarianism in the political realm, but also atheism, specific views on art, meta-ethics and so on. It is not necessary to endorse all of those things in order to be a libertarian.
From my meager understanding of Objectivism, it is very similar to the libertarianism of the American Libertarian Party (i.e. right-libertarianism), meaning they are both essentially liberal ideologies; libertarians of this ilk even frequently don the "classical liberal" label. As I understand it, Objectivists want government, but only insofar as it exists to protect natural rights (which were not granted by God because Objectivism is inherently atheistic). In contrast, right-libertarians are divided as to whether government should exist at all (the minarchist-anarchist debate). I think both favor
laissez-faire capitalism, but that's where their overlap ends. As Humes fork stated, whereas right-libertarians are more open (for a lack of a better word) to other opinions, Objectivists tack on additional values, including metaphysical objectivism, physicalism, and moral realism. There are probably more, but I'm not familiar enough with Objectivism to enumerate them all.
TL;DR: What Humes fork said.
