Your graduate school expenses do not count for the American Opportunity credit, the one that can pay you cash over and above tax you had withheld from a  paycheck.  The undergraduate classes can count for the American Opportunity credit but the largest portion of it, $1500, can only reduce your taxable income to zero, not pay you additional cash.  The Lifetime Learning credit, which can be taken for graduate expenses, can also only reduce your taxable income to zero, but does not pay you anything after that.  So, the graduate expenses may not be worth anything to you, if you don't have enough taxable income to use that credit.