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.