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The theory of quasiconformal and quasiregular mappings in R", n= 2, has resulted from efforts to generalize the theory of conformal mappings and analytic functions of one complex variable (cf. the survey article [50]). The systematic study of n-dimensional quasiconformal mappings, ie one-to-one quasiregular mappings, was started in 1960 by FW Gehring and J. Väisälä. The study of nonhomeomorphic n-dimensional quasiregular mappings was started by Yu. G. Reshetnyak in 1966. The usual methods of the classical complex analysis such as. those based on geometric or algebraic special properties of complex numbers (power series, infinite or finite sums and products, complex integration) are not applicable to the study of quasiregular mappings in R", n= 3. The case n= 2 is somewhat exceptional because in this case one can apply some powerful results, which have no counterpart in the higher dimensional …