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This monographis a self-contained exposition of the definition and properties of functionsof bounded variation and their various generalizations; the analyticalproperties of nonlinear composition operators in spaces of such functions;applications to Fourier analysis, nonlinear integral equations, andboundary value problems.It is written for non-specialists and gives a readable overall acount of the theory, methods, and applications. The bookis written for non-specialists and gives a readable overall acount of the theory, methods, and applications. Every chapter closes with a list of exercises and open problems. Thusthe book serves as a fruitful sourcefor further research.