review) but the reader will Emd (at the end of the review) a set of references to existing studies on more complex systems. (C) 2001 Published by Elsevier Science B.V.We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory. [References: 343]
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