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This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.