I received a $500 gift certificate for re-attending school. Would I include that in my tuition expenses or not?

 If the school gave you a gift certificate for attending, that is a discount in your tuition. The income is not taxable, however, you have to reduce any education credit that you claim by the amount of the tuition discount. For example, if tuition was normally $5000, and you receive a $500 discount, you would report that you paid $4500. 

But a gift certificate for what exactly?  Something like a prepaid debit card might be taxable if it can be used for anything. I liken this to (1) a gift card given by a landlord to a tenant who renews his lease, or (2) a gift card given by  a bank to a customer who renews his CD.  Form 1099-MISC is generally issued for those.

It was paid directly towards the tuition. It was incentive to re-attend. They took $500 off via a gift certificate

Then Opus 17'ss answer is correct.