Breakup problems please HELP!!

I broke up with my boyfriend two days ago. I was really happy about the breakup but now things in my head are complicated because he is still extremely persistant. I broke up with him because we have been in a cycle of arguing and I didn't feel mentally free for a long time. He has been verbally abusive before(calling me dumb, a bitch, I should kill myself). He did apologize but he says he would be gentle and everytime he says that it never happens along with other things he does. We were together for a year and a half. He says he understands that and that he's changed and he keeps coming to my house. Yesterday he came with a surprise of printed out photos. I told him after we broke up that we need space and he did not seem to get that and now things in my head are more complicated and I know I had feelings for him but after him doing this my head is thinking one way and my intuition is saying another and I feel stressed. I told him that he really needs to give me space because it frustrates me that I don't have it seems like he finally understood. I don't know if it's normal to feel kind of good that your exboyfriend is still chasing you after you breakup. But it definitely complicated things in my head. If anyone out there can help clarify how I'm feeling or relate please let me know. Is it part of the breakup process or should I tell him to seriously back out of my life. I know he's really hurt but he never did things like this when we were together. Only now as my mom says is his "desperate move". Please help!