It is the first world war, second world war (avoid writing “before the war” or “after the war” when you mean the second world war).
Also use hundred years war (it actually lasted 116 years, from 1337 to 1453), war of Spanish Succession, civil war (England), American civil war, Spanish civil war, Crimean/Boer/Korean/Vietnam war.
Also note six-day war, Gulf war (1991), Iraq war (2003), Afghan war (2001), Falklands war (1982, not Falklands conflict).
