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This book presents a comprehensive account of the  renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view.

It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature.

The book begins with the basic notion of the RG theory, including its connection...