I am 24 and in a relationship with this guy from my college for about an year. For the first 4-5 months things went on really well because we were in different places but after that I moved to the same city and things took an ugly turn. Whenever he was angry and I did not listen to him, not matter how small the issue is; he would shout at me, ask me get out of his apartment at 3 in the night and other verbal abuses. I too would say things in anger to which he tells me not to answer him back.

There were ups and down but for last few months things have been really ugly. He would abuse me and my family (to which I answer back) and then he would go one more level down calling me a Slut, linking me with every guy I know. I have been very honest in the relationship but I cannot take abuses. And for him he loves me a lot but when he is angry he just goes out of control. He would come to my place at 4 in the night to say sorry and if I tell him that I do not wish to talk to him, he will again abuse me.

I don't know if I should continue with this relationship?

No. Get out. Without anger management classes these behaviors do not get any better over time. They will get worse including physical abuse. Life is too short to put up with him. Set your standards higher. You don't deserve to be treated this way.

All relationships are great in the beginning, but as you learn more about him, the less you like. His words of apology, or yours for that matter no longer match and until things change they get worse. Maybe its time to re evaluate and take the appropriate actions that will work for you. I would have been gone and moved to better things long ago.

Clearly you see that your reaction is not the right one, nor is his actions the right ones for you. I guess the honeymoon is over. You could try just listening to him and see what results that brings. If that doesn't work and you cannot talk and resolve your issues, then its time to go. More often than not, relationships run their course, and partner spend a lot of time not letting them go, and trying to bring the good times back.

Oliver and tal both deserve greenies but my submit button still doesn't work.
The only way this trait will ever change is to get worse as time goes by,