Hi everyone!

I'm a 23-year-old female student at a university in Michigan. I got a new prof this year for one of my courses, a guy in his mid-30s I became interested in over the last couple months.
When I would sit in his lecture in the front row he would keep looking at me for a longer period of time and I would return his glances but rather expressionless. You know, not like smiling or anything. I would just look attentively.
A week ago I paid him a visit at his office during his office hours to have a little chat with him about the lectures in general. I came in and he greeted me with an overwhelmingly radiant smile (couldn't find a cheesier word, sorry). That bastard made me forget my own name Must be some kind of super power. So I sat down and we talked about 40 minutes and a little past his office hour. He did most of the talking making sure to explain his answers thoroughly (Jesus, did this guy talk). What I observed about him while listening is that his pupils were damn big. Like truck tires (I hope he ain't using or something). When he was done talking I wanted to thank him and leave but he asked me how my project was going (everyone in this course got the same project for which we have a couple months to work on) and if I needed any help. I answered that I haven't got started yet so he offered me to come again after Christmas Break so he could help me. I was a little surprised about this offer since it's not his job to help us with the project but the teaching assistants'. You know, the boring work is for the inferiors. Again, I wanted to leave and he asked me if I have any other questions so we talked again about some other crap. This time, I even got on my feet and put my jacket on but he started talking again. Maybe he craved some company, I don't know. I know though, that there are a lot of female students who would love to keep him company. I smiled and offered him my hand to shake and thanked him for his time. He smiled back and invited me once more to come back after Christmas break and I finally left.
Now brace yourself for some teenage stuff: the reason I wanted to leave so badly was that I felt highly nervous in his presence. The good kind of nervous. When I walked out of his office I actually had to sit on the nearest bench because my legs got wobbly. I don't like being like that cause it makes it hard to think clearly and that's how bad decisions are born.
I would like to drop by again. However, I dislike asking for help and prefer to take care of my school stuff by myself. I could have a little conversation with my pride and kindly ask it to stay out of this at least once.
As you have probably figured out by now I do like that guy and would like to get to know him better preferably outside the classroom. I don't see him primarily as a professor or somebody superior to me as I don't perceive anybody that way. I mean, we're all just humans, right? At the end of the day we don't differ that much. So yeah, I primarily perceive him as a guy who seems interesting to me.
Please also note, that our university policy DOES NOT forbid student-professor relationships.

So, what do you guys think? Does his behavior in any way indicate interest? Do you have experienced something similar or have any other kind of advice for me?

PS: The guy ain't married, already checked.

I appreciate any serious answer and advice.
Thank you,

Strangeland