Agfa record III solinar

On the 105mm solinar from the agfa record III, does the front element screw apart to focus? Or does the whole front element unscrew?

I've been trying to separate the front element, thinking that is the way it focuses. But I have not been able to.

It is front element focus. Weather or not it unscrews completely I can't answer. It is not unusual for the lubricant used by Agfa to almost solidify over the years.
I recently had mine serviced by Certo 6(?).

As Bob said the front group screws in/out to focus. It does completely unscrew from the shutter but to do this the ring with distance markings must be removed. It has three little screws around the perimeter which mate it to the actual front lens group. Make sure to set the lens to infinity first (if possible) and note the position of the distance ring, front element, and shutter or you'll have to re-calibrate it during reassembly. It took several days sitting in acetone for the grease to un-seize enough for me to remove the front group and then a few more days to properly collimate the lens when I realized my mistake.
The Solinar has a really lovely rendering on black and white which makes all the work worth it.