I'm having problems understanding Hodge duality in its most basic form. It relates exterior p forms to exterior n-p forms where n is the dimensionality of the manifold. I cant seem to follow the discussion on the hodge dual operator on this lecture course (page 19): http://www.damtp.cam.ac.uk/user/gr/about/members/dgnotes3.pdf How does the star operator bring about all the Faraday 2-form example? Any help would be appreciated. Thanks.