Why do I catch him staring at me, then he quickly looks away?

Hello,

If somebody is staring at you but looks away quickly when you notice, it's probably because they don't want you to notice that they are staring at you.

This could be for a number of reasons. Firstly, it sounds like he is conscious of the fact the is staring at you, i.e. It's not by accident, in which case he may have a more dazed look on his face and perhaps pause or smile when you notice. 

The fact that he looks away quickly seems to suggest he is embarrassed of the fact he is doing so. He may be staring at you because he likes you, i.e. Has some feelings for you, or perhaps because he finds you attractive and/or intriguing.

Perhaps the best way to find out is to talk to him.

I hope this helps.