I agree with a PP that it's important you should tell people: your family, friends, university staff and yes, even the police if he doesn't knock it off PDQ.
Should this escalate into stalking you need as much sunlight on it as possible. I have extensive experience of this horribly invasive crime (lucky me, eh?), as I've been at the receiving end twice. On the first occasion I was a little younger than you are now, and no one had even invented the term 'stalking' yet. Certainly the police didn't take it seriously (they still don't take it seriously enough, but it was even worse then). Document everything. And whatever you do, don't pick up those calls. If you do, you've just taught him he has to leave days' worth of abusive messages in order to get you to answer, and he will ramp it up. What you need to give him back is precisely nothing, until he gets tired of arguing with a machine.
Don't protect this abuser with your silence. The more people who know what you're experiencing, the more they'll be able to look out for your welfare.
The above insight is hard-earned. I've suffered at the hands of these kinds of soul-sucking vampires more than once. Not all of them were partners, either, just pathetic little men with an axe to grind against women or who can't or won't take 'No' for an answer. This 'man' has shown you exactly who he is, and he's irrefutably one of these people. I can promise you, they don't change. Remember this if your resolve ever starts to waver (and keep posting here; the good women of MN will help you bolster it if necessary.)
I applaud your strength. Be vigilant. 