It looks like burnt on crud. Usually it will come of with glass cooktop cleaner, as others have mentioned, the Weiman brand usually works fine. If none of the aforementioned techniques work, you can very, very, very, very, very carefully take a razor blade to it and scrape the junk off. You must be very^5 careful not to scratch the glass.
It may take some work if the previous owners just kept cooking over it. My parents own a couple summer rental houses In Rhode Island. In my younger years it was my job to make sure they were cleaned up between renters. Every so often I'd come across a mess like that. People who have never owned a glass cooktop don't know how to take care of them. ~8 years ago these people
destroyed a brand new $1000 GE glass cooktop (separate from the oven) trying to clean melted/burnt on sugar with steel wool, a metal putty knife, and God knows what else.
Alternatively:
1. Use it as a negotiating point.
2. Remove old stove
3. Replace a nice gas Viking gas range.