  We investigate how current and proposed observations of neutron stars can
lead to an understanding of the state of their interiors and the key unknowns:
the typical neutron star radius and the neutron star maximum mass. A
theoretical analysis of neutron star structure, including general relativistic
limits to mass, compactness, and spin rates is made. We consider observations
made not only with photons, ranging from radio waves to X-rays, but also those
involving neutrinos and gravity waves. We detail how precision determinations
of structural properties would lead to significant restrictions on the poorly
understood equation of state near and beyond the equilibrium density of nuclear
matter.
