The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper "Diophantine approximation onabelian varieties," Ann. Math.133 (1991) and together givean approach to the proof that is accessible to Ph.D-levelstudents in number theory and algebraic geometry. Eachchapter is based on an instructional lecture given by itsauthor ata special conference for graduate students, on thetopic of Faltings' paper.

A comprehensive, graduate-level treatment of unit equations and their various applications.

The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.