So I 'think' I like this girl... how should I approach her?

[Joe]

Now, I say I 'think' I like her because I don't actually don't know her lol and neither does she know me. The first time I saw her I just thought she was really pretty, so you could say I'm only into her looks as of now, but I want to get to know her.

I only see her 3 times a week just before one of the lectures I have with her. I considered going up to her and saying 'Hi' and introducing myself and let the rest flow like a river. Today I even had a chance to sit next to her, but I didn't which I regret a lot. I only avoided to do so because I was with two of my friends (who are guys) and knowing them they'd probably nudge me then do the eyebrow raise and make me nervous and stuff (you know what I mean hopefully), oh and of course I hesitated a bit because I was probably shy.

There is one issue though... As I've said I only see her before a certain lecture 3 times a week and I've never seen her around other than those times. Every time, I see her with a guy who she talks and sits next to in every lecture, but I don't know who he is to her. Although I'm at least 75% sure he's not her boyfriend. I'm judging from the way they talk to each other, how they look at each other, etc. But hey... I don't have a PhD in body language lol.

So yeah, help me out here please