My definitions.  Likely to change as my education continues.

act of war – an action that provokes a declaration of war.  For example, invading another country prompts them to declare war in return, as do their allies (prompting casus foederis).  No longer a meaningful legal term.

casus belli – a cause of war.  An act or event that prompts a declaration of war or is used as an excuse for war (the stated reasons may not be the real reasons).  Wikipedia.

casus foederis or casus fœderis – when an ally is drawn in, such as occurred with the Great War and such as NATO uses in defence of its members.

declaration of war – to politely and formally inform another party that you intend to kill them before attempting to do so.  How terribly, terribly quaint.  Wikipedia.  Often applied after the bombers have taken off and just before the bombs are dropped.

deontology – Greek for duty is deon, .  A moral theory where one puts duty before consequences.  Deontologists say some actions are always impermissible, such as those violating human rights.

jus ad bellum – the agreed reasons for war.

jus in bello – the agreed acceptable wartime conduct.

Just War Theory – theologian legal philosophers making excuses for warmongers to kill by claiming it conforms to the teachings of their church, when it clearly doesn’t in anyone else’s eyes.  Wikipedia.

law of war – if there’s one thing worse than war, it is unrestrained war.  If I sound sarcastic, I don’t mean to.  Covers the reasons for starting a war and behaviour during it.  Wikipedia.

Westphalian sovereignty – the principle that each nation state has sovereignty over its internal affairs and that all nation states are equal.  Seems to be collapsing this past few decades as superpowers ‘police’ ‘unruly’ states.  Wikipedia.  I think this is the principle being referred to in DD101’s assertion that the state is entitled to the monopoly on using violence against its citizens.

irenology – peace studies (from irenic meaning aiming for or aimed at peace).  Not recognised by my spell-checker 🙁

eirenicon – a proposal made as a means of achieving peace.

polemology – the study of human conflict and war, the opposite of irenology

modus vivendi – an agreed arrangement to allow co-existence despite differences of opinion (from Latin for ‘a way of living’).  Wikipedia.