With a record number of voters dissatisfied with the two major parties' candidates, third parties are gaining popularity. Among these, the largest is the Libertarian party, whose candidate, former New Mexico governor Gary Johnson, is already polling in the double digits. It's not too hard to see why, as Libertarianism is essentially a fusion of the Democratic party's social liberalism with the Republican party's fiscal conservatism. So, while the Libertarian party is still distinct from the major parties, it's similar enough to attract those who are disillusioned with them. With Libertarianism making such growth into the culture, it will be helpful to briefly discuss some of the core tenets of Libertarian philosophy.
The basic core of Libertarianism is the belief that government should have as limited a role as possible, but government still plays a basic, servile role, as opposed to Anarchy. It is out of this core belief that the two major aspects of Libertarianism grow- social liberalism and fiscal conservatism. The social-liberal aspect of Libertarianism is largely born out of the desire to keep government from meddling with people's private lives, with gay marriage being the most obvious example. The Libertarian party has always held that government has no right to define what constitutes a "proper marriage," and has supported gay rights. The fiscal conservative aspect believes that government should stay out of business, and should cut taxes wherever possible. This aspect seems to be the most controversial, and has often lead to the charge that Libertarians are greedy. However, Libertarians themselves hold that they believe people should be free to keep whatever money they make, rather than give such a large part of it to the government. So, if somebody wanted to give this money to charity, they would actually have more to give.
Obviously, this hardly scratches the surface, as there are many more aspects of Libertarian thought, and many disagreements and points of view among Libertarians themselves. However, this is the basic core element- that limited government benefits people most- that unites the party amidst its various disagreements.