The 13 chapters of this book centre around the proof of
Theorem 1 of Faltings' paper "Diophantine approximation on
abelian varieties", Ann. Math.133 (1991) and together give
an approach to the proof that is accessible to Ph.D-level
students in number theory and algebraic geometry. Each
chapter is based on an instructional lecture given by its
author ata special conference for graduate students, on the
topic of Faltings' paper.