Most libertarians are not fans of Ayn Rand, contrary to one definition on this site, although many admire her writings.

A libertarian is someone who believes in the primacy of individual rights. A Libertarian (with capital L) is someone who is a member of the U.S. Libertarian party, founded in 1972.

Libertarians (both big and small L) are people who argue that human beings are ends-in-themselves, that they have rights (either natural, consequential, or existential) and who argue that these rights precede government. Because rights precede government, libertarians argue that there are things that government may not do. As a consequence, libertarians describe a very small sphere for government, are advocates of free markets, and are defenders of individual liberty. Libertarians also are advocates of peace (and have been, throughout history, at the forefront of peace movements) and nonintervention.

Some libertarians can best be described as anarchists - that is they think that the best government is no government.