No A3 is equivalent to A-. Aaa is Moody's equivalent to triple-A.
You have to know about how sovereign ratings work a little bit too, but "A3" is Moody's shorthand for "AAA."
You are right. A3 is not the highest. Aa1 would be the highest. A3 is the next thing to a B grade, but without being a B, which is a subjective judgement in my book.