The Hope Credit applies for the first two years of post-secondary education. It can be worth up to $1,650 per student, per year. A credit of 100 percent of the first $1,100 of qualified tuition and related fees paid by the student is eligible during the tax year, plus 50 percent of the next $1,100. And the student must be enrolled at least halftime for at least one academic period which began during the year.

The Lifetime Learning Credit applies regardless of the number of years the student is in the post-secondary program. This credit equals 20 percent of the first $10,000 of tuition and fees paid by the student during the year.
However, a student cannot claim both the Hope and Lifetime Learning Credits for the same year. The credits can be claimed by the parent or the student, but not both. And students who are claimed as a dependent cannot claim the credit.
For more information, you can visit www.irs.gov and look up Publication 970, Tax Benefits for Education.