What does it mean when I catch him staring at me, then he keeps staring at me but he doesn't look away?

No.
He's trying to initiate a staring contest, and he smiles because he knows when he has won.

Seriously. I would say yes, can't think of any other reason to be so attentive.

he definitely likes you,but maybe he is shy.or wants to be sure of your feelings as well, in order to decide to bring your friendship into another level or not.
stare more at him and start to act more feminine and sweet when you are close to him.
wish you the best luck.

Girl, if he is looking at you and doesn't bother to look away when you catch him doing it, it's because he finds you attractive and is not the shy type to look away when the girl catches him. When he looks at you, and smiles, look back at him and smile. That will give him a sign that you're open to his flirting and that you are attracted to him too. Try finding a way to talk to him in private where it's just you and him. Maybe then it'll be easier for you guys to communicate your attraction and feelings towards one another.

He's staring at you like that because he finds you attractive in some way. If I were you I'd smile and stare right back at him. Flirt a little if you're interested and make sure that he knows that he has a chance if he decides to stop staring and finally start talking to you. :)

Well hun, it really sounds like he is either trying to get your attention besides just the staring. Have you tried just talking to him in private, maybe ask him out for a date. You do understand that you can play the dominant one and ask him out on a date. I wish I would have done it in high school and asked my friend out and found out than that he liked me and found me intriguing and than I wouldn't be in the predicament with an engagement and in serious like with another guy. I suggest next time you two our together but alone together, ask him if he would like to go on a date to like a movie or dinner where the two of you can talk personal. Hope this helps.