The non-aggression axiom is the fundamental tenet of libertarian and anarchist thought. I will define it here in my own words:
No person has the right to forcefully take the life or property of another unless in self-defense.
In case my definition is not clear, here are some other great words on the matter:
Walter Block: “It shall be legal for anyone to do anything he wants, provided only that he not initiate (or threaten) violence against the person or legitimately owned property of another.”
Murray Rothbard: “No one may threaten or commit violence (‘aggress’) against another man’s person or property. Violence may be employed only against the man who commits such violence; that is, only defensively against the aggressive violence of another. In short, no violence may be employed against a nonaggressor. Here is the fundamental rule from which can be deduced the entire corpus of libertarian theory.”
Thomas Jefferson to Francis Gilmer, 1816: “No man has a natural right to commit aggression on the equal rights of another, and this is all from which the laws ought to restrain him.”