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Rating: 
Summary: Plenty of material; conisely written
Review: This title is no lie; readers interested in loops / knots / gauge theories *OR* quantum gravity can gain from reading this text, but to do so some skipping around is needed. On the other hand, the programme of quantum gravity associated with the Ashtekhar's ``new variables" is carefully and clearly laid down in this monograph; that is how this reviewer read the text --- straight through in search of the results associated with the new variables. The going can be tough at times in the initial sections, which outline the group of loops and holonomy theory but that strain is only temporary since readers are rewarded in their investment by a thorough practice section that casts Yang Mills theory in the space of loops before turning to QG itself. At times in discussions of ``loop quantum gravity" the question of where kinematics ends and dynamics begins can be obscure, but not so in this text. Further, where the programme is successful is spelled out clearly. However, the programme of loop quantum gravity has adjusted somewhat since publication of this text (particularly with respect to rigorous proof of the existence of the loop transform, selection of an inner product on the Hilbert space of states, and spin foams --- which are *not* overcomplete) so readers should be warned that there is more to this story. But what is presented in this text is more then enough to whet readers appetites. In short, this text is well worth the effort for readers seeking to understand the `loop QG' programme.
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