Need some advice  

Ribbon-stripe African mahogany veneer
with what appears to be solid edging. Your second photo looks like maybe there is a piece of the edging split off and missing?
It's possible that an experienced restorer, depending on the finish, could re-amalgamate the original surface film without messing up the color for not too much expense.
I rather like your little table. An elegant interpretation of a traditional form with pleasing proportions.

Thanks for the response. ...
Thanks for the response. Yes, the edge is solid wood and In the second photo, next to the seam (if that's the right word) there is a diagonal line which might just look like a scratch but is actually a crack. There isn't any wood missing ,though. I guess I can get an estimate from a restorer easily enough. Just wondering if refinishing devalues it?

A clean crack can be easily glued and/or filled.
If it's convenient, taking the table to the restorer will help one to estimate how involved treatment might be. A simple spot test of solvents on the underside should determine such in minutes.
With treatments like this, less is always more, but, if done properly, it will only enhance the piece's value. If we were discussing an 18th century high-style American piece, I might recommend doing nothing or consulting a conservator instead.
Good luck. Cute table!
P.S.
Woody:
hahahahahahahaha
I said, "clean crack"!

Thank you! I've written to a...
Thank you! I've written to a restorer nearby who specializes in mid-century.