'This book by two leading theoretical computer scientists provides a comprehensive, insightful and mathematically precise overview of computational complexity theory, ranging from early foundational work to emerging areas such as quantum computation and hardness of approximation. It will serve the needs of a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the ... Read moremathematical foundations of computer science. I will keep it at my side as a useful reference for my own teaching and research.' Richard M. Karp, University of California at Berkeley 'This text is a major achievement that brings together all of the important developments in complexity theory. Student and researchers alike will find it to be an immensely useful resource.' Michael Sipser, author of Introduction to the Theory of Computation 'Computational complexity theory is at the core of theoretical computer science research. This book contains essentially all of the (many) exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field.' Avi Wigderson, Professor, Institute for Advanced Study, Princeton This text is a major achievement that brings together all of the important developments in complexity theory. Student and researchers alike will find it to be an immensely useful resource. Michael Sipser, MIT, author of Introduction to the Theory of Computation Computational complexity theory is at the core of theoretical computer science research. This book contains essentially all of the (many) exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field. Avi Wigderson, Professor, Institute for Advanced Study, Princeton This book by two leading theoretical computer scientists provides a comprehensive,insightful and mathematically precise overview of computational complexity theory, ranging from early foundational work to emerging areas such as quantum computation and hardness of approximation. It will serve the needs of a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the mathematical foundations of computer science. I will keep it at my side as a useful reference for my own teaching and research. Richard M. Karp, University Professor, University of California at Berkeley The reviewer's impressions are that this new textbook on computational complexity is available for a very attractive price and that on Amazon it may be verified that it has received very good reviews by several leaders in this field (Karp, Sipser, Wigderson). Ulrich Tamm, Mathematical Reviews Show Less