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The purpose of this book is to present a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. The modulus method was initiated by Arne Beurling and Lars Ahlfors to study conformal mappings, and later this method was extended and enhanced by several others. The techniques are geometric and they have turned out to be an indispensable tool in the study of quasiconformal and quasiregular mappings as well as their generalizations. The book is based on recent research papers and extends the modulus method beyond the classical applications of the modulus techniques presented in many monographs.

Boundary value problems. --- Hausdorff measures. --- Moduli theory. --- Quasiconformal mappings. --- Quasiconformal mappings --- Moduli theory --- Calculus --- Applied Mathematics --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Theory of moduli --- Mappings, Quasiconformal --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Conformal mapping --- Functions of complex variables --- Geometric function theory --- Mappings (Mathematics) --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology