The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early 1970s and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the 1990s progress has been made in this field, which includes the development of alternative formulations of the approach and powerful techniques for solving the exact renormalization group equations, as well as widening the scope of the exact renormalization group method to include fermions and gauge fields. In particular, the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.
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