You'll need to take your strings off.
Then lift the nut out (you'll find it's loose, that's why it's gone like that!)
Then apply a LITTLE woodglue or PVA glue to the nut slot.
Put the nut back in the right place (make sure it's the right way round, I've glued stuff in wrong before...not a good feeling)
Use a small clamp to keep the nut in place while the glue dries. Clamp it so pressure is applied downwards, pushing the nut to the bottom of the slot.
Make sure the nut hasn't slid to the left or right during clamping.
Use a cloth to wipe any excess glue.
Make sure again that the nut hasn't moved.
Leave for 24 hours, then and only then put your strings back.
Should be like new!
