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
addresses a topic that is not only rich mathematically, using a
large variety of techniques in mathematical analysis, but is also
one with strong ties to current experiments on ultra-cold Bose
gases and Bose-Einstein condensation. The book provides a
pedagogical entry into an active area of ongoing research for both
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
mechanics.