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Rational Points is written by Gerd Faltings and published by Springer Science & Business Media. It's available with International Standard Book Number or ISBN identification 3322803406 (ISBN 10) and 9783322803405 (ISBN 13).
This book consists of the notes from the seminar Bonn/ Wuppertal 1983/ 84 on Arithmetic Geometry. It contains a proof for the Mordell conjecture and may be useful as an introduction to Arakelov's point of view in diophantine geometry. The third edition includes an appendix in which a detailed survey on the spectacular recent developments in arithmetic algebraic geometry is given. These beautiful new results have their roots in the material covered by this book.