Talk to Me Like I'm Stupid: The Right of Self-Defense

I was doing some digging yesterday and came across Thomas Hobbes' Leviathan, which--me, being a college drop-out and all--I haven't read. Anyway, I was intrigued by his natural laws, particularly this first one...

that every man ought to endeavour peace, as far as he has hope of obtaining it; and when he cannot obtain it, that he may seek and use all helps and advantages of war.

This came to me while I was trying to do some research on the roots of the right of personal self-defense. Put differently, how have the legal and philosophical arguments evolved in terms of the right of a person to defend their person against violence? Was this always true in Western societies? Was it always true of women? What, traditionally, have been the limits? And how important is the right of self-defense to a functional social contract? And finally, am I just reading Thomas Hobbes all wrong? Us college drop-outs tend to do that...

As an aside, I'd ask that those of us without some real knowledge on these questions hold back on posting--unless it's to ask a question. I'd like to keep this as focused as possible. I'm not interested in your beef with the NRA.