<human>: Summarize the given text in a few sentences.

I (24M) have been talking with a girl (24F) for about two months now. Initially it was getting to know each other, about 3 weeks ago we kissed and have only made out with each other on a few occasions. 

A few weeks in to talking to her she tells me that she just got out of a long relationship, 3+ years, with a guy that she thought she was going to marry, and she wasn't sure what she wanted (understandably so). He dumped her out of the blue (I'd say they have been broken up ~4.5 months now). 

A couple days ago I brought up a talk about how she was doing and where things were headed with us. In person, she told me she is not over her ex, but likes what we are doing and wants to keep doing that (that's okay with me). She texted me later that night explaining that she wasn't over her ex and wasn't ready for a serious relationship though. When we hang out she sometimes seems like her head isn't all there, she's preoccupied, or she isn't really interested in finding out more about me(basically she's still thinking about the ex I feel). It's hard to explain. Other times we hang out we have a lot of fun with each other. Since this talk though we have hung out with each other in a group of other friends.

The shitty part is I really like her. I haven't been in a relationship for about 8 months. This girl is my type physically, I like what she's about and think she's great. But I know being dumped unexpectedly sucks and it takes time to get over an ex, especially when she wanted to marry the guy. 

I don't know what to do. I want to remain friends and hope she'll come around, but my brain tells me that's not going to happen and to quit dreaming. Should I stop initiating hanging out/talking with her and give her more space? Should I keep pursuing her? If there any women out there that I can get an opinion from, that would be great.
<bot>: Don't know if I should stop contacting a girl that I'm really interested in who isn't over her ex from about 4.5 months ago.