The long-awaited detection of a gravitational wave from the merger of a binary neutron star in August 2017 (GW170817) marked the beginning of the new field of multi-messenger gravitational wave astronomy. By exploiting the extracted tidal deformations of the two neutron stars from the late inspiral phase of GW170817, it was possible to constrain several global properties of the equation of state of neutron star matter. By means of fully general-relativistic hydrodynamic simulations, it is possible to get an insight into the hydrodynamic evolution of matter and into the structure of the space-time deformation caused by the remnant of binary neutron star merger. Neutron star mergers represent an optimal astrophysical laboratory to investigate the phase transition from confined hadronic matter to deconfined quark matter. With future gravitational wave detectors, it will most likely be possible in the near future to investigate the hadron-quark phase transition by analyzing the spectrum of the post-merger gravitational wave of the differentially rotating hypermassive hybrid star. In contrast to hypermassive neutron stars, these highly differentially rotating objects contain deconfined strange quark matter in their slowly rotating inner region.