Includes bibliographical references and index.

Deterministic protocols -- Rank -- Randomized protocols -- Numbers on foreheads -- Discrepancy -- Information -- Compressing communication -- Lifting -- Circuits and proofs -- Memory size -- Data structures -- Extension complexity of polytopes -- Distributed computing.

"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 disjointed 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. Part I presents basic theory in a clear and illustrative way, offering beginners an entry into the field. Part II 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"--