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Understanding the equation of state (EOS) of neutron-rich matter is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of energetic heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova all depend critically on the nuclear-matter EOS. In this contribution I focus on the EOS of cold baryonic matter with special emphasis on its impact on the structure, dynamics, and composition of neutron stars. In particular, I discuss how laboratory experiments on neutron skins as well as on Pygmy and Giant resonances can help us elucidate the structure of these fascinating objects.

Isoscalar monopole and dipole compressional modes are computed for a variety of closed-shell nuclei in a relativistic random-phase approximation to three different parametrizations of the Walecka model with scalar self-interactions. Particular emphasis is placed on the role of self-consistency which by itself, and with little else, guarantees the decoupling of the spurious isoscalar-dipole strength from the physical response and the conservation of the vector current. A powerful new relation is introduced to quantify the violation of the vector current in terms of various ground-state form factors. For the isoscalar-dipole mode two distinct regions are clearly identified: (i) a high-energy component that is sensitive to the size of the nucleus and scales with the compressibility of the model and (ii) a low-energy component that is insensitivity to the nuclear compressibility. A fairly good description of both compressional modes is obtained by using a "soft" parametrization having a compression modulus of K = 224 MeV.

Laboratory experiments sensitive to the density dependence of the symmetry energy may place stringent constraints on the equation of state of neutron-rich matter and, thus, on the structure, dynamics, and composition of neutron stars. Understanding the equation of state of neutron-rich matter is a central goal of nuclear physics that cuts across a variety of disciplines. In this contribution I focus on how laboratory experiments on neutron skins and on both Pygmy and Giant resonances can help us elucidate the structure of neutron stars.