How would I put a finish on this maple wood kitchen table?

I have a maple wood kitchen table with a shiny smooth finish that allows for hot and cold items placed on it and not leave a burn mark.

The table is 27 years old, the same as me. A hand me down.

The finish on the table top lately seems to be peeling. I am assuming due to the aging of the wood and finish.

How would I re-coat it to look new again? Would I have to sand it down or what would be the process?How would I put a finish on this maple wood kitchen table?
I believe this can help you with your table.