I will introduce languages of imperfect information (introduced by Hintikka and Sandu in 1989) and several competing approaches to model the dependence and independence of logical operators. I will also say something about the phenomenon of signalling and its applications to Lewis signalling games and B. Skyrms' extending signalling games. The main focus will be on the Nash equilibria semantics (Sandu and Sevenster) and some of its applications.