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 both the integer and fractional case. It includes up
to date presentations of the tunneling and metrology experiments
related to the quantum Hall effect. It will serve the community of
physicists and mathematicians at professional or graduate student
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