2nd date and no kiss?

Ok, so I'll try to make this short...ish

I got out of a longterm relation with my first bf not too long ago, and I'm completely clueless to how the dating world goes... or so it seems.

I met him at school, he's one of the tutors. I liked him from the beginning, he's good at what he does, he likes it etc. We talked a bit, not sure if it was flirting or just friendly. Anyways, I decide to have some fun and go for the challenge (he's the first guy that got my interested since my breakup) and so I contacted him on Facebook, with a witty comment on something we talked about at school. Now, before you tell me I should stay away from the teachers... There's only a couple of years difference between us, both adults, and I'm done with the project. The university is big and there's no way we would run into each other at school.

So... a couple of weeks of texting back and forth (convos initiated by both of us). A bit of flirting (but nothing REALLY obvious). He hinted a couple of times that we should actually meet (example: "long story, i'll tell you in person, at one point"). He finally decides to ask me out... really last minute. He invited me to a show (at which he hinted a couple of days before, asked me if I like that kind of music etc... but never asked me straight up if I want to go... and I wasn't going to invite myself). So the night of the show he tells me that he'll go only if a "certain someone" wants to go with him... and I accept (didn't have any plans and I assume he's pretty shy and he won't ask me again if I refuse him). He picked me up, refused to let me pay for tickets (he reserved 2 tickets already... ) and drinks. We had fun, talked, danced a bit. Dropped me off... but didn't try to kiss me... or I completely didn't see it?

Another week passes by... he reminds me that i promised him some drinks at one point (in one of our earlier convos), and asks me when I'm free. We set a time for the next day, he picks me up, but we end up going for dinner instead (told him didn't really feel like going for drinks, I was sick). He ends up paying again for dinner since it was drinks that I owe him, not dinner. We walked together for a bit and i grabbed his arm, since it was icy and I was scared of falling (that's the most I'm ok with doing... the rest I'm expecting him to initiate). So... Again, nice "date" but no kiss at the end (not even on the cheek)... Is he shy? Is it because I was sick (but at least you would go for a hug, no?). Are we just hanging out? I can't tell and it annoys me! (not enough to go straight and ask him, though). Help:( What do you guys think?

ps: we are supposed to finally go for those drinks after the holidays (we both have other engagements till then)