Does this boy likes me?

I like a boy at my school and I think I was a little obvious when we first met. I froze and kept staring and smiling at him like an idiot! xD I started (among with other students) taking lessons with him after school. All the time while he's explaining he just looks at me (Not that much at the other students) Yesterday when he was going to say goodbye he came very close and whispered in my ear "give me a kiss". Today when we were going to say goodbye he surrounded me with his arm while giving me a kiss in the cheek. I started walking down the hall and he called my name. When I went to him he said "Maybe if you want you could go to my house and study together".
The day after that we were talking alone before the lessons got started, and in one point he just shut up and kept looking into my eyes. During the class he kept making jokes and he looked at me as if to see if I was laughing. He gave me his phone number. After class was finished he walked with me. We were walking so close our hands almost touching and sometimes he did the same than before (shut up and looked into my eyes). Then we kissed and said goodbye.

He's very friendly with everyone and I don't know if he likes me or if he's like that just with everybody. What do you think? Should I make a move? I'm dying to kiss him, but I don't want to throw it up. How can I give him a hint? A subtle insinuation?