Windsor 2019: Dynamics of Complex Quantum Systems, 5-8 August 2019, sponsored by CCPQ. This workshop, the 7th in the series, is designed to bring together UK + European theory and experimental groups involved in realising, simulating and modelling the dynamics of a variety of complex quantum systems. The meeting is aimed at discussing both new mathematical and computational methods, as well as new experimental applications/phenomena/physics at a level suitable for postgraduate students in the field. Topics of interest include, but are not limited to: cold atoms optical lattices, quantum materials and nanomechanical oscillators in cavities, phase transitions, coherence and entanglement, interferometry and atom optics, superfluidity, non-equilibrium dynamics, spinor and exotic condensates, quantum information applications, experimental perspectives. The extra day for the workshop is dedicated to special sessions on numerical simulation of strongly correlated systems including tensor network methods, environment engineering for quantum computation, cold atoms for quantum simulations and novel architectures for quantum computation and simulation.