Rather shy & unexperienced guy, what am I supposed to do?

Hey. I met this guy at university some time ago and can't just forget about him. At first I thought he didn't like me that much, but somehow we sit together during almost every lecture. Even when there's seats available, he comes and sits right next to me.

But however, his behavior is so ambivalent. One day, he is all nice, we kind of cling to each other (or I do this to him?). The next day he is different. He avoids being alone with me, but approaches me when I am with a friend or in a group. When I am talking to him, sometimes, there is like some chemistry going on between us. And as if his eyes were kind of speaking to me, you know? I enjoy it, but he goes only farther away the next day. Then he would be around his male friends, but sits in close proximity, often behind me.

I am a bunch of years older than him (7) and I assume he has never had a relationship before. We do a lot of stuff together with a friend of ours. And he remembers details about what I said, mirrors my actions as I do mirror his sometimes.

But he also isn't into texting, he would text all his male friends but not me. He seems nervous around me as well. I sometimes watch him from the corner of the eye when we're sitting close and he looks stiff and not very relaxed. He is not in contact with any other girls so much, but he behaves different around me. I really like talking to him and I assume he does too, but when we are left alone, sometimes he just kind of fled the scene.

I really do like him, but I don't know what to do. When I try to ignore him, it feels like he comes back towards me, but when I do approach him too fast, he would kind of run away. What is your opinion? I've met with him and a friend before, but I don't want to ask him about a date, because he kind of declined going to have lunch with me last year. I am not sure why he did that. I don't want to bother him, but I feel it in my gut that there is something mutual, although it's different. What should I do? Am I wrong?

Updates
8 mo
Thanks for your replys so far. I've already got his number due to (organizational) uni stuff. But we seldomly text. I want to know, is he even interested in me? Even if he finds me attractive, nonetheless he could just not want a relationship right now.

I don't want to ruin our relationship, friendship whatsover and create an awkward situation, if he sees us just as colleagues. He seems very polite, even in texting. But we also have times when we laugh a lot together in between lectures.
Rather shy & unexperienced guy, what am I supposed to do?
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