What are the three degrees of priesthood?

There are actually only two priesthoods, the first is the Aaronic named after the brother of Moses, Aaron. Within that priesthood are three offices that of Deacon, Teacher and Priest. The other priesthood or higher priesthood is the Melchizadeck priesthood named after the righteous king of the same name. Within that higher priesthood one may hold the office of Elder or High Priest.