adverb Used to concede a point or to express acknowledgment or awareness, often before stating some contrasting or competing information; used as an expression of respect to the point in question.
He's a good student and usually does well. Granted, he did fail that one test, but I think there were good reasons for that.
adjective used to mark the premise of a syllogistic argument
Granted that he has done nothing wrong, he should be set free.