I've driven many hydrostatic mowers and lawn tractors - but I've never taken one apart until today!
The basic job of this transmission (and the concept of Hydrostatic power) is converting constant velocity power through a hydraulic pump into a matching hydraulic motor with a variable speed.
But to see the process and the parts...
That's a whole new level of understanding.
Here is a link that was shown to me with an excellent animation of the fluid flow process since it's impossible to operate with the transmission disassembled -https://www.youtube.com/watch?v=qxZFSNITK-c.
Enjoy!