difference between convert -quality and convert -resize and convert -density

I'm trying to reduce file size of a .png in the terminal with Imagemagick convert Does anyone know the difference between convert -quality , convert -resize and convert -density ? convert -quality does not seem to work at all, whether you give it 99, 30, 10 or 1. It changes the file size sometimes even making it bigger! This is a file of about 10MB. I am trying to bring it down to perhaps 1MB. I am scared that convert -resize might do something to it such that if someone goes to print it out it will not be the size of an A4 page anymore.