Difficult / Aggressivee person at work. How to deal with it?

I just started working somewhere and there is a person there who is acting shady right from the start. She keeps observing me, coming to me and starting weird conversations, talking about me loud in front of everybody and generally trying to make me look bad. It weird because it is very straightforward etc, normally people have some respect etc... I dont know. I just ignore that person 100% etc and stay away, but I dont want something like that to continue. Would you go into conflict or just keep ignoring that no matter what. How to get on the top of the situation? Thanks.