Libertarianism is a philosophy that opposes action by force. That fundamental kernel of an idea results in a very wide array of beliefs, ranging from anarchist communism which outlaws private property to libertarian socialism that places everything in an open trust to free market capitalism which places everything in the hands of individuals. Less common are polycentric laws and transhumanist libertarian movements. In the end, the key binding idea is that it is wrong to assert control by force over an unwilling fellow person.
See also Anarchy