If you’d like to read a survey article or two on presupposition, here are the two best ones (one more philosophical, the other more technical):

• Scott Soames: 1989. “Presupposition” in: D. Gabbay and F. Guenthner (eds.) Handbook of Philosophical Logic: Volume IV: Topics in the Philosophy of Language. Dordrecht: Kluwer Academic Publishers. pp. 553-616.
• David Ian Beaver: 1997. “Presupposition” in Johan van Benthem and Alice ter Meulen (eds.) Handbook of Logic and Language. Amsterdam: Elsevier. pp. 939-1008. Preprint: .

If you want to study the notion of common ground, here are three references to look at (and you can then follow the references mentioned in these works):

• Herbert H. Clark: 1996. Using Language. Cambridge University Press.
• Ronald Fagin, Joseph Y. Halpern, Yoram Moses, Moshe Y. Vardi: 1995. Reasoning about Knowledge. MIT Press.
• Robert Stalnaker: 2002. “Common Ground”. Linguistics and Philosophy 25(5-6), December 2002, 701-721. doi:10.1023/A:1020867916902