What to do about this girl?

Hi, so there is this girl at my uni course who I really started to like, which is rare because I have a hard time to fall in love. She is in my so "group" at uni and we have a lot of classes together and also more recently study together with 2-3 more friends. Now, I never had a girlfriend nor ANY experience with girls (I'm 21) and don't know how on earth to approach her. She sometimes writes me on Facebook and texts me, but at uni she seems a bit uninterested at times. This makes it a bit harder for me to tell whether she might actually like me back, which I really doubt. So before you say "just ask her out", I'm way to insecure for that, I'd rather try and find out subtly if she likes me or is even remotely interested. How do I achieve that? I appreciate any help, since this is really dragging me down!

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