Can wine go bad? What to do with an open wine bottle if there is still wine left?

I was having a feast yesterday and my friend and I took a bottle of wine to drink. We didn’t drink all of it (there’s around half of the bottle left) and I now have an open bottle of wine. Is there a way to preserve that wine somehow? It was sealed with that wooden-like thing that made a pop sound and I can’t shove it back again.

So, what do I do with an open bottle if wine? Can I seal it somehow so that the wine can’t go bad (if it does)? Will it be drinkable later?
Or do I throw it away?

the bottle remained open for the night, if that changes things.