The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture •  Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.

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Pei-Chu Hu, Shandong University, Jinan, China; Chung-Chun Yang, Hong Kong University of Science and Technology, China.

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