No, you cannot claim a deduction or credit for tuition paid for a previous year. You can only claim tuition for classes that start in the same year or in the first three months of the following year. On your 2018 tax return you can only claim tuition for classes that start in 2018 or in the first three months of 2019. You cannot claim tuition you paid in 2018 for classes that you took in 2017. And you can only claim tuition in the year you actually pay it. So tuition that you paid in 2018 cannot be claimed on your 2017 tax return, even though it was for classes in 2017.