Neutron stars are compact objects formed in cataclysmic astrophysical events known as supernovae. They have masses about twice that of the Sun and a radius approximately 10 to 15 kilometers resulting in densities on the nuclear scale. They have temperatures up to 10¹² Kelvin and can have surface magnetic fields up to approximately 10¹⁵ Gauss. Since the publication of the pioneering papers from R. C. Tolman (Tolman 1939) and J. R. Oppenheimer and G. M. Volkoff (Oppenheimer and Volkoff 1939), conventional models of non-rotating neutron stars assume they are perfect spheres. However, due to high magnetic fields, certain classes of neutron stars such as magnetars and neutron stars containing color-superconducting quark matter cores are expected to be deformed (non-spherical). In this thesis, we seek to examine the stellar structure of such objects in the framework of general relativity. Non-spherical models are obtained by deriving the stellar structure equations that govern deformed neutron stars. First, we present a one dimensional parameterized model where we introduce a deformation constant which dictates the degree of deformation. Second, we present a two dimensional stellar structure model where the deformation of neutron stars is governed by anisotropies in the equation of state. From these two models, we calculate stellar properties such as masses and radii, along with pressure and density profiles and investigate any changes from standard spherical models.
