Best sources for communication complexity
Books:


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.)


Articles:


Alexander Razborov, "Communication Complexity".


Lecture Notes:


Toni Pitassi, "Communication Complexity, Information Complexity and Applications", 2012
Ran Raz, "Circuit Complexity and Communication Complexity".


Also check Sasha's remarks about communication complexity.