Why would a guy continuously sneak glances at a girl?

There is this guy I have been getting to know lately who I have caught looking at me several times. He is shy (I am pretty outgoing) and, like me, he has never dated anyone before. Whenever we are in class together and I look his way I notice he is already looking at me. As our eyes meet, he and I smile (sometimes holding the gaze for a few moments longer) then look away. This will happen numerous times when we are around eachother, but I am unsure of the reasoning behind this action. Is it because of attraction or something else? What are other signs that a shy guy may be interested in a girl?
I know this is a frequently asked question, but I thought to ask because I really do like this guy and hope it works out.
Why would a guy continuously sneak glances at a girl?
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