What is a Libertarian?
Libertarians believe that you have the right to live your life as you wish, without the government interfering -- as long as you don't violate the rights of others. Politically, this means Libertarians favor rolling back the size and cost of government, and eliminating laws that stifle the economy and control people's personal choices.
Are Libertarians liberal or conservative?
Libertarians are neither. Unlike liberals or conservatives, Libertarians advocate a high degree of both personal and economic liberty. For example, Libertarians agree with conservatives about freedom in economic matters, so we're in favor of lowering taxes, slashing bureaucratic regulation of business, and charitable -- rather than government -- welfare. But Libertarians also agree with liberals on personal tolerance, so we're in favor of people's right to choose their own personal habits and lifestyles.
Often people say that Libertarians are liberal on personal issues and conservative of economic issues, or that Libertarians "borrow" from both sides; however, Libertarians are consistently and identifiably libertarian on both personal issues and economic issues, recognizing that the most prosperous, peaceful, and tranquil country is built upon the maximization of liberty instead of government force. Libertarians stand on the side of liberty on political issues, without the exceptions and broken promises of Republican and Democratic politicians. This is why the Libertarian Party is called the Party of Principle.
What is the guiding Principle for Libertarians?
The guiding Principle which underpins many libertarians' stance on personal and economic issues can be boiled down to one sentence: "I will not initiate force or fraud against another." This is known as the Non-Initiation of Force Principle or the Non-Aggression Principle. Abiding by this principle is the key to living a free and prosperous life, as, at its core, it recognizes the individuality, the humanity, and the sovereignty of each individual. On the political front, Libertarians hold government to this same standard, that of non-initiation of force or fraud, for if each of us, individually, may not initiate force against another, a just government as an expression of the will of many individuals, may not initiate force either.
For a more detailed presentation describing this Principle, and how it informs Libertarian thought, please see the excellent An Introduction to the Philosophy of Liberty animation