Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.

‘This looks like an essential resource for any student who wants to understand deterministic and randomized communication complexity deeply.'

Scott Aaronson - University of Texas

'Communication complexity is not only a beautiful and important area of the theory of computing, it is also vibrant and ever-changing. Two of the leading researchers in this area take us through a fascinating journey into the theory and applications of communication complexity and through old and new jams. I feel inspired to teach a course based on this book and help spread the word.'

Omer Reingold - Stanford University, California

'This book is a much-needed introductory text on communication complexity. It will bring the reader up to speed on both classical and more recent lower bound techniques, and on key application areas. An invaluable resource for anyone interested in complexity theory.'

Mark Braverman - Princeton University, New Jersey

‘… a great book … relevant to advanced undergrads and graduate students alike, while the more advanced topics will also be of interest to researchers …’

Michael Cadilhac Source: SIGACT News Book review column

‘… must-have reference for students but will be welcomed by researchers as well because it is so well-written and aptly organized … Highly recommended.’

A. Misseldine Source: CHOICE