Relaxation processes in many-body quantum systems arise in many diverse areas of physics ranging from inflation in the early universe to the emergence of classical properties in complex quantum systems. Ultracold atoms provide a unique opportunity for studying non-equilibrium quantum systems in the laboratory. The coherent quantum evolution can be observed on experimentally accessible timescales and the tunability in interaction, temperature and dimensionality allows the realization of a multitude of different relevant physical situations.Through building specific model systems we propose to study a wide variety of non-equilibrium quantum dynamics under conditions ranging from weakly interacting to strongly correlated, from weakly disturbed to quantum turbulent and search for universal properties in non-equilibrium quantum evolution.We address questions of de-coherence in a split many-body system and the concomitant emergence of classical properties. We will study the fate of the highly entangled quantum states that are created when a system in its excited state decays. Systems with instabilities and controlled quenches will give us insight into the creation of defects and excitations. We will experiment with bosons, fermions and mixtures, and take advantage of the rich internal structure of the atoms. Our systems will also be observed when interacting with ‘baths’, which can be internal or external with controlled coupling and can be engineered from simple thermal to squeezed, from large to mesoscopic with non-Markovian properties.Our ultimate goal is insight into the answers to fundamental questions: What does it take for an isolated many-body quantum system with a set of conserved quantities to relax to an equilibrium state? Which universal properties and scaling laws govern its evolution? Can classical physics and thermodynamics emerge from quantum physics through the dynamics of complex many-body systems?