The Libertarian movement is an extreme right wing movement.Everybody seems to think that, but I don't believe it to be the case. A better statement is that "Libertarians are right of Right and left of Left". So depending on your existing world-view, you would probably see the Libertarians as either radically Leftist or radically Rightist, and - in either case - you'd be partially correct and partially wrong.
For example, Libertarians align with the left, and would go further than the standard American Left on many social issues:
Abortion - Libertarians tend to be pro-choice and the LP platform specifically says that the State should not be involved in making those decisions.
Drug laws - a typical American "Leftist" position might be "legalize marijuana". A Libertarian position would be more like "The State has no authority whatsoever to regulate what you put into your own body. End ALL drug laws".
Death Penalty - Libertarians are generally opposed to the death penalty.
Gay marriage / minority rights - Libertarians believe the Govt. should have no say in marriage at all, which implies that homosexual couples should be able to marry if they want. Of course, it also implies that others should be free to choose not to recognize that marriage, but hey... that's the price of freedom: You want to be free, you can't compel other people to behave the way you want them to.
OTOH, yes, Libertarians tend to be more closely aligned with "the Right" on economic issues: taxation, trade, business regulation, etc. But I don't think it's fair to call the Libertarian movement "an extreme right wing movement". If for no other reason, because a simple "left / right" dichotomy is not a valid model for representing political orientation.