This thesis explores ultracold quantum gases of bosonic and fermionic atoms in optical lattices. The highly controllable experimental setting discussed in this work, has opened the door to new insights into static and dynamical properties of ultracold quantum matter. One of the highlights reported here is the development and application of a novel time-resolved spectroscopy technique for quantum many-body systems. By following the dynamical evolution of a many-body system after a quantum quench, the author shows how the important energy scales of the underlying Hamiltonian can be measured...

This remarkable volume showcases the latest advances in a rapidly growing field of research. The author's treatment of ultracold quantum gases of bosonic and fermionic atoms in optical lattices includes new insights into the nature of ultracold quantum matter.