  Multi-messenger observations of neutron star (NS) mergers have the potential
to revolutionize nuclear astrophysics. They will improve our understanding of
nucleosynthesis, provide insights about the equation of state (EOS) of
strongly-interacting matter at high densities, and enable tests of the theory
of gravity and of dark matter. Here, we focus on the EOS, where both
gravitational waves (GWs) from neutron-star mergers and X-ray observations from
space-based detectors such as NICER will provide more stringent constraints on
the structure of neutron stars. Furthermore, recent advances in nuclear theory
have enabled reliable calculations of the EOS at low densities using effective
field theory based Hamiltonians and advanced techniques to solve the quantum
many-body problem. In this paper, we address how the first observation of GWs
from GW170817 can be combined with modern calculations of the EOS to extract
useful insights about the EOS of matter encountered inside neutron stars. We
analyze the impact of various uncertainties, the role of phase transitions in
the NS core, and discuss how future observations will improve our understanding
of dense matter.
