A while ago someone (not Jewish) "lent" me a notebook, to use in class, because one day I did not have one. She did not say it was a gift. However, it is something you use to write on it, so you surely cannot give it back to the original owner in its original state. I used it only for that day, so some pages are still blank. Moreover, I am pretty sure she forgot of it. Do I still have the halachic obligation to give it back to that person?

Shalom Ralph, Firstly, allow me to admire the fact that you are as meticulous and caring about mitzvot between man and his fellow, as between man and God, for both are religious obligations! You definitely should return the rest of the notebook, for the common practice is to lend pages to fellow students, but not to give an entire notebook. In addition, to not return it may inadvertently cause a chilul Hashem (a desecration of God's Name), for Jews must set an example and be at least (!) as morally careful as is commonly accepted, that she shouldn't go around saying, or even thinking, that Jews don't act properly. To the contrary, by returning it you are doing a Kiddush Hashem (sanctifying His Name), by doing positive "public relations" for God and His People, in addition to cleaning your conscience, your soul, and your "bank account" from any non-kosher property. With Love of Israel, Rav Ari Shvat