There are many libertarians, affiliated with either major political party, or voting mostly as independents. There is also a Libertarian Party (LP for short), but its numbers are far less than the number of American who self-identify as libertarians.
Like many small parties, the LP lacks some of the structure and formality of the two major American political parties. It also attracts a collection of colorful, sometimes just unusual, political candidates.
Over at Reason magazine (but available online), Dave Weigel has an article on the upcoming Libertarian Party nomination fight: “Who’s Going to Get Your Wasted Vote? A guide to the wildest Libertarian Party nomination fight in decades.”
Weigel predicts that former GOP congressman Bob Barr will get the nomination, but he highlights over half a dozen other contenders.