Gaussian States in Quantum Information

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These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A special emphasis has been given to the phase space analysis of quantum dynamics and to the role of Gaussian states in continuous variable quantum information.