There are various statements of the non-aggression principle (abbreviated NAP, or ZAP, Zero-Aggression Principle) (Wikipedia). I like Rothbard's statement of it:
- "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."
This statement is good for specifically calling out self-defense. Note that aggression is against person or property (since a person owns themselves, there's some redundancy there). Frequently phrases like "the initiation of force is wrong" (or "aggression" for force) are used; initiation makes it clear that self-defense is not considered wrong; self-defense also includes hiring agents to defend you (although they have no special rights).
It is not specifically spelled out in the NAP, but libertarian thought usually allows only for commensurate defensive response (killing someone for stealing a loaf of bread, except in extreme circumstances, would likely be considered initiation and not response). The idea is to use necessary force to stop a threat—not pull punches, but neither cruelty or continued force when the threat is neutralized are part of self-defense.
Also external to the NAP is the idea of justice after the fact. Rothbard's "infringe as you were infringed", Block's "two teeth for a tooth", and Kinsella's "applied estoppel" principle are all good sources here. Please see the sources for (but not the paper itself as it is somewhat narrow in focus) my paper.