Let me explain what I mean. When I was was in college I took a class in the history of France from the middle ages to present day. The first thing the professor did was have each of us bring in a map of France that we had drawn with our own hands. Nothing to fancy. It included the basic shape, the major rivers, the major cities and towns, and the the borders.
Looking back it was a very good idea. At least one had a sense of being orientated when reading material. It was well worth the 20 minutes it took to put a blank sheet of paper over a map in a book and copy it.

I would like to find an application that does this. Not one that copies the map itself. But one that can place a translucent or transparent page over an existing map and allow the user to trace (draw) the maps features themselves.

Please let me know if any such thing exists. And to those of you that are in school and taking some class about China, the mid-east, or anywhere, let me recommend that exercise. It seems silly. But it really is useful.

Thanks in advance for any information. (Obviously, I want it to run on Linux)

You can use any graphics program that supports layers. Load your map, then create a new, transulcent layer over it. The GIMP can do this.