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There is a fascinating connection between abstract mathematical theories and measurable physical phenomena. The emerging complexity of many-particles in interaction demands new mathematical theories. A mathematical description of a system often suggests or predicts new phenomena never measured before. This book beautifully describes an area where this interplay has been the active backbone of many successful stories in many-particle physics such as superconductivity, magnetism, and Bose condensation. It has been my inspiration since I started reading it in graduate school and its importance grew because over the years the author became my mentor, colleague, and friend.