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In the last years a growing attention has been dedicated to many body quantum systems from the point of view of quantum information. Indeed, after the initial investigation of simple systems as single or two qubits, the need of understanding the characteristics of a realistic quantum information device leads necessarily to the study of many body quantum systems. These studies are also driven by the very fast development of experiments which in the last years reach the goal of coherent control of a few qubits (ion traps, charge qubits, etc.) with a roadmap for further scaling and improvement of coherent control and manipulation techniques.§This book gives a selection of current research topics in the field of quantum information for many body quantum systems together with open problems.