Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics. He is the James and Carol Collins Chair of mathematics at UCLA and the youngest person ever to be promoted to full professor at the age of 24. In 2006 Tao became the youngest ever mathematician to win the Fields Medal. His other honours include the George Polya Prize from the Society for Industrial and Applied Mathematics (2010), the Alan T Waterman Award from the National Science Foundation (2008), the SASTRA Ramanujan Prize (2006), the Clay Research Award from the Clay Mathematical Institute (2003), the Bocher Memorial Prize from the American Mathematical Society (2002) and the Salem Prize (2000).

• Expansion in Cayley graphsExpander graphs: Basic theoryExpansion in Cayley graphs, and Kazhdan's property (T)Quasirandom groupsThe Balog-Szemeredi-Gowers lemma, and the Bourgain-Gamburd expansion machineProduct theorems, pivot arguments, and the Larsen-Pink non-concentration inequalityNon-concentration in subgroupsSieving and expandersRelated articlesCayley graphs the algebra of groupsThe Lang-Weil boundThe spectral theorem and its converses for unbounded self-adjoint operatorsNotes on Lie algebrasNotes on groups of Lie typeBibliographyIndex

Asymptotic group theory is a recently emerging branch of group theory, that can be described as the study of groups whose order is finite—but large! Tao’s book is certainly a valuable introduction to that exciting new subject." - Alain Valette, Jahresbericht der Deutschen Mathematiker-Vereinigung