This book contains a unique survey of the mathematically
rigorous results about the quantum-mechanical many-body problem
that have been obtained by the authors in the past seven years. It
is a topic that is not only rich mathematically, using a large
variety of techniques in mathematical analysis, but it is also one
with strong ties to current experiments on ultra-cold Bose gases
and Bose-Einstein condensation. It is an active subject of ongoing
research, and this book provides a pedagogical entry into the field
for graduate students and researchers. It is an outgrowth of a
course given by the authors for graduate students and post-doctoral
researchers at the Oberwolfach Research Institute in 2004. The book
also provides a coherent summary of the field and a reference for
mathematicians and physicists active in research on quantum
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