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This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul):  "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.

Arithmetic. --- Connections (Mathematics). --- Galois theory. --- Geometry. --- Ordered sets. --- Galois theory --- Arithmetic --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematics. --- Algebraic geometry. --- Algebra. --- Field theory (Physics). --- Group theory. --- Algebraic Geometry. --- Field Theory and Polynomials. --- Group Theory and Generalizations. --- Euclid's Elements --- Set theory --- Calculators --- Numbers, Real --- Equations, Theory of --- Group theory --- Number theory --- Geometry, algebraic. --- Groups, Theory of --- Substitutions (Mathematics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Algebraic geometry --- Mathematical analysis

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This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul):  "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.

Group theory --- Algebraic geometry --- Geometry --- Mathematics --- Classical mechanics. Field theory --- landmeetkunde --- wiskunde --- mechanica --- geometrie

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Mathematics