In this book we discuss how to exploit strong correlations among ultracold atoms in order to create novel, exotic quantum states. In the first two chapters, we devise dynamical out-of-equilibrium preparation schemes which lead to intriguing final states. Most importantly, we propose to create the elusive supersolid state via a quantum quench protocol. Supersolids - quantum hybrids exhibiting both superflow and solidity - have been envisioned long ago, but have not been demonstrated in experiment so far. Our proposal to create a supersolid state is perfectly accessible with current technology...