The thematic school Gravitational wave emission from proto-neutron stars and neutron star mergers (GWsNS-2023) is a graduate school that will cover several aspects of the gravitational wave (GW) emission from neutron stars. Lectures will mainly focus on the gravitational emission from supernovae, proto-neutron stars and coalescing binaries, with an eye on the connection between astrophysical phenomena and the equation of state (EOS) of dense matter that defines the structure and macroscopic behaviour of these compact objects.