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Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update of the most recent developments. It offers a comprehensive introduction to this fascinating topic, that will certainly become an essential reference for anybody working in this field. Rationality problems have been of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems have motivated significant developments, as for example the theory of abelian integrals, Riemann surfaces and the Abel-Jacobi map; This work is aimed at researchers and graduate students in algebraic geometry.This work is aimed at researchers and graduate students in algebraic geometry