The Poincare Seminar is held twice a year at the Institut Henri Poincare in Paris. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental results are covered, with some historical background. Particular care is devoted to the pedagogical nature of the presentation. This volume is devoted to the quantum Hall effect. After a historical and general presentation by Nobel prize winner Klaus von Klitzing, discoverer of this effect, the volume proceeds with reviews on the mathematics and physics of...