Many students are surprised to learn that they don't actually own their research notebook. Depending on the institution's rules, your PI might not even own it--it could be considered property of your college or university.
Some PIs are fine with students making their own copies of a notebook at the end of their research experience, but others are not. Regardless, most will require you to leave the original copies in the lab for a variety of reasons.
If your research mentor or PI hasn't specifically addressed who has official ownership of your notebook, make a point to ask before the end of the semester. It's not critical information--because the answer won't change your research life--but you should still know the answer.