I used to know a libertarian–at least that’s what he called himself. In his mind, the only valid functions of governments were police forces and armed forces. In particular, no government should build roads. You want to build a street in front of your house? Build it and charge a toll to anyone who uses it. If you and your neighbors agree to build a string of such streets and make a private company to charge just one toll to use it, fine. No business of the government’s. I never thought to ask him why the government should provide police services when you and your neighbors could always hire your own police force.
Well, that was the way he wanted to live; not me.
As mentioned above there are many varieties of libertarianism.