The lower picture on the left makes the anvil appear to be a wrought or malleable iron anvil of the type that would have had a hardened steel plate forge welded or cast into the top.
That plate appears to be fractured and broken to a significant degree on at least one long side of the top edge, and the anvil body has been impacted to enough of a degree to have caused the anvil body to get deformed.
The only way to properly fix that anvil, would be to remove the rest of the steel plate, make a new steel plate, forge weld the new plate to the top of the anvil body, and then reharden and temper the top.
Unless you make less than minimum wage, it would be easier and cheaper to buy a bew anvil, and you would wind up with a far better anvil.