How to progress with a shy guy?

There's a shy guy that I like I think likes me back. He stares when I'm not looking and always facing me in the classroom/cafeteria. He also uses my name a lot, loses train of thought, stutters, and touches his face talking to me. He also put his leg against my leg and held it there for about 15 minutes once while we were studying. He also waits for me to leave the classroom then follows me out which is kinda weird. However, we only study together and it's awkward when we run into each other outside of class/studying. How should I progress things with this shy guy? Should I wait for him to make the moves and just be receptive?
How to progress with a shy guy?
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