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Although there are many books on finite size scaling in classical statistical mechanics, there is not a book on finite size scaling in quantum mechanics. This work is one of the first to describe quantum critical phenomena and quantum phase transitions in atomic and molecular physics. It shows how finite size scaling can be used to analyze important phenomena that are difficult to analyze using other methods. The book also includes a general description of near-threshold phenomena for quantum few-body problems with special emphasis on atomic and molecular applications, such as ionization, dissociation, and some aspects of resonance phenomena.