Learn Swedish: Jag ser inget smör i kylskåpet. - I see no butter in the fridge.

Inget is describing the noun smör (butter). The word for "no" or "not any" has to match the gender of the noun it belongs to. Because smör is an ett word (ett smör), we use the neuter form inget. If it were an en word, we would use ingen, and for plurals we would use inga.

Wait, doesn't inget usually mean "nothing"? Why does it mean "no" here?

It can mean both! When used completely on its own, inget (or ingenting) means "nothing". But when you put it directly in front of a noun, like in inget smör, it acts as a describing word meaning "no" or "not any".

Could I use inte (not) in this sentence instead?

Yes, but you would need to add något (any) to make it sound natural. You could say Jag ser inte något smör (I do not see any butter). Using inget is simply a shorter, very common way of saying the exact same thing.

Why does kylskåpet end in -et?