For both undergraduate and graduate students:
Up to $5,500 per year in Perkins Loans for undergraduates and up to $8,000 for graduates depending on your financial need, the amount of other aid you receive, and the availability of funds at your college or career school. The college is the lender.
$3,500-$5,500 in Direct Subsidized Loans depending on grade level and financial need; and $5,500-$20,500 in Direct Unsubsidized Loans depending on year in college and dependency status, with no requirement to establish financial need. The Department of Education is the lender.
For parents of dependent undergraduate students and for graduate students, Direct PLUS Loans are available for up to the cost of attendance minus any financial aid the student receives. The Department of Education is the lender.
Also see https://studentaid.ed.gov/types/loans.