Anarcho-capitalism (also known as “libertarian anarchy” or “market anarchism” or “free market anarchism” or “private-property anarchism”) is a form of anarchism that eliminates the state in favor of individual sovereignty in a free market. It is regarded as the most extreme form of libertarianism.
Other libertarians, although they believe in as small a government as possible, still believe that some government is necessary - to provide for national defence, to prosecute crime, and to provide a court system to settle legal disputes peacefully. Anarcho-capitalists believe that all these government functions can be performed by competing private companies. Thus, private national defence companies would provide protection against foreign invasion; private police forces would catch criminals; private courts would decide legal cases. However, it is unclear how any of this could actually work in practice.