What are some of the best sources (books and papers) to motivate and learn communication complexity on its own and in connection with its relation to computational complexity theory?
Eyal Kushilevitz and Noam Nisan, "Communication Complexity", 2006.
Stasys Jukna, "Boolean Function Complexity: Advances and Frontiers", 2012. (Part II of the book is dedicated to Communication Complexity.)
- Alexander Razborov, "Communication Complexity".
Toni Pitassi, "Communication Complexity, Information Complexity and Applications", 2012
Ran Raz, "Circuit Complexity and Communication Complexity".
Also check Sasha's remarks about communication complexity.