The finish is probably an oil based varnish. To properly refinish the top, you need to sand it smooth(not necessarily sanding off the old finish) and apply three coats of varnish according to the instructions on the can.

You may elect to do a 'repair', but as a rule, short cuts last a short time or create more problems later.

I sanded the top where there were some rings from cups and the bare wood and then used amber shellac for a new finish, then paste wax on top of that. I didn't remove all of the old finish but am happy with the way the shellac blended with the original finish. Someday I may completely refinish the desk but I just don't have the time right now - I can use it now the way it is. You can see the great shape it's in (see linked photo). Thanks for your suggestion.

Here is a link that might be useful: {{!gwi}}