Diophantine Equations and Approximation -- Diophantine Approximation and its Applications -- Roth’s Theorem -- The Subspace Theorem of W.M. Schmidt -- Heights on Abelian Varieties -- D. Mumford’s “A Remark on Mordell’s Conjecture” -- Ample Line Bundles and Intersection Theory -- The Product Theorem -- Geometric Part of Faltings’s Proof -- Faltings’s Version of Siegel’s Lemma -- Arithmetic Part of Faltings’s Proof -- Points of Degree d on Curves over Number Fields -- “The” General Case of S. Lang’s Conjecture (after Faltings).

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.