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This textbook introduces geometric measure theory through the notion of currents. Currents—continuous linear functionals on spaces of differential forms—are a natural language in which to formulate various types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics * Provides considerable background material for the student Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for use in the classroom and for self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for graduate students and researchers.

Mathematics. --- Measure and Integration. --- Integral Equations. --- Integral Transforms, Operational Calculus. --- Geometry. --- Differential Geometry. --- Convex and Discrete Geometry. --- Integral equations. --- Integral Transforms. --- Discrete groups. --- Global differential geometry. --- Mathématiques --- Equations intégrales --- Géométrie --- Groupes discrets --- Géométrie différentielle globale --- Geometric measure theory --- Currents (Calculus of variations) --- Currents (Calculus of variations). --- Geometric measure theory. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Integral currents --- Normal currents --- Integral transforms. --- Operational calculus. --- Measure theory. --- Convex geometry. --- Discrete geometry. --- Differential geometry. --- Calculus of variations --- Measure theory --- Groups, Discrete --- Infinite groups --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Equations, Integral --- Functional equations --- Functional analysis --- Math --- Science --- Geometry, Differential --- Euclid's Elements --- Discrete mathematics --- Convex geometry . --- Geometry --- Combinatorial geometry --- Operational calculus --- Differential equations --- Electric circuits --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Differential geometry