I have been unable to find a good reference for a book that study in details ergodic theory on sub shifts of finite type in dimension $D>1.$ The only reference that I got was actually a book by Gerhard Keller, Ergodic States in Ergodic Theory, London mathematical society, Student Text 42. However, it is a bit difficult to read, and sometimes becomes too general (too motivated by physics phenomenons), and not too much symbolic as I would like to see.



The Book for ergodic theory on SFT in dimension $D>1.$
I don't think there are many books that deal with this. Is there a particular topic or direction you want to go in? Some areas of papers: 


Algebraic SFTs have been treated by Kitchens, Schmidt and others; 


Decidability and aperiodicity issues have been treated by Berger, Robinson, Kari, Culik and others;


Entropy issues by Hochman, Meyerovitch, Sahin, Pavlov, Robinson, Desai, Schraudner and others. 


