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.