The INFN Research Network (Iniziativa Specifica) QUANTUM involves 9 research groups affiliated with 6 INFN Divisions: Bari, Bologna-Camerino, Catania-Palermo, Milano (Como), Napoli-Salerno and Trieste. The research activity focuses on the outstanding recent developments that have changed the status of Quantum Mechanics, for instance in the emerging fields of Quantum Information and Quantum Technologies. The major objective of QUANTUM is the investigation of typical quantum mechanical effects and phenomena via three major, interrelated avenues: Entanglement and other Quantum Correlations, Quantum Dissipative Systems and Quantum Control. The topics investigated have a foundational character, but are of interest also in view of possible applications. We mention the links of entanglement with complexity, its key role in quantum phase transitions, and its appearance in neutrino oscillations and particle decay (Kaon systems). Moreover, the dissipative dynamics due to quantum fluctuations in many-body systems, the quantum-to-classical transition, the phase-space (Wigner function) formulations, the Casimir effect, the dynamical evolutions of cold gases and Bose-Einstein condensates. Finally, the emerging field of quantum tomography and quantum process characterization, quantum channels, time reversibility and conservation laws, the mechanisms to improve the efficiency of elementary thermodynamic quantum machines, sub-shot-noise imaging and quantum metrology. The theoretical effort is interdisciplinary and highly synergic, involving close collaborations among the partners, exchange of students, post-docs and young researchers, and the use of analytical techniques from quantum field theory, statistical mechanics and quantum information theory.