Explicit methods in number theory. Rational points and Diophantine equations.
Résumé
This volume contains a selection of seven short courses in number theory taught during a special trimester at Institut Henri Poincaré (from September to December 2004), centered on Diophantine equations and how to effectively solve them. The lectures, targeted at second year graduate students, display an attractive panorama of mathematical ideas and tools, that can be used to reach this goal.