A breif synopsis of libertarianism:1. What is a libertarian?
The word means roughly "believer in liberty". Libertarians believe in individual conscience and individual choice, and reject the use of force or fraud to compel others except in direct response to force or fraud. Some libertarians (the so-called Le Fevbrians) reject *all* use of force, even in self-defense.

2. What do libertarians want to do? Help individuals take more control over their own lives. Take the state (and other self-appointed representatives of "society") out of private decisions. Put both halves of the welfare/warfare bureaucracy out of business and liberate the 7/8ths of our wealth that's now soaked up by the costs of a bloated and ineffective government to make us all richer and freer. (This presupposes that everyone has some wealth which is not the case) Oppose tyranny everywhere, whether it's the obvious variety driven by greed and power-lust or the subtler, "well-intentioned" kinds that coerce people "for their own good" but against their will.

3. Where does libertarianism come from?
Modern libertarianism has multiple roots. An important one is the minimal-government republicanism of the U.S.'s founding revolutionaries, especially Thomas Jefferson and the Anti-Federalists. Adam Smith, John Stuart Mill and the "classical liberals" of the eighteenth and nineteenth centuries were another influence. More recently, Ayn Rand's philosophy of "ethical egoism" and the "Austrian School" of free-market economics (This only benefits the wealthiest 10%) have both contributed important ideas. Libertarianism is alone among 20th-century radical movements in owing virtually nothing to Marxism.
It does have some good principles, but the wider view is akin to anarchy.