I. Heights II. Weil heights III. Linear tori IV. Small points V. The unit equation VI. Roth's theorem VII. The subspace theorem VIII. Abelian varieties IX. Neron-Tate heights X. The Mordell-Weil theorem XI. Faltings theorem XII. The ABC-conjecture XIII. Nevanlinna theory XIV. The Vojta conjectures Appendix A. Algebraic geometry Appendix B. Ramification Appendix C. Geometry of numbers Bibliography Glossary of notation Index.