I have been seeing a gentleman for several months. We grew up together in our home town. I moved to one city, he moved to another. In July we met up for the first time. I was previously married and he asked about the former husband. After explaining that we are no longer together, he understood and his name has not come up since. It had been when I would visit him in his city, we would always meet at a hotel. He always answers the telephone when I am around him no matter what gender is on the other side. He explains to them that he is with his Lady Friend and will have to get back to them. The last time we were together he took me by his apartment, not for sex but to get some changing clothes. We hung out there for awhile without him feeling the least bit nervous. That is something that had never been discussed before. He treats me with much respect.
Am I imagining things or is there something to this? I am not use to this dating thing and was only wondering if I am on to something.

Sounds like a position of "Wait and see" If that was Me I'd be happy with the way things are progressing.

Don't over think it, just let the ball roll. There's no need to try and predict the future, or even worry about it for that matter.

It sounds like a nice friendship and as others have said,I would wait and see.
Perhaps he is waiting for you to make the first move considering the fact that you may be still healing from your breakup.
If you want more or are concerned where this may be going I would simply ask.It is the only way to truly know if there is a future for romance or if you will remain friends.

See how you feel in a year, until then, enjoy getting to know some one, and try not to get carried away with a good feeling.