This course deals with special topics in theoretical cosmology from a selection related to the mathematical aspects of cosmology to the more physical aspects. Examples of topics would include the role of symmetries in obtaining cosmological solutions to the Einstein field equations, the structure and possible necessity of singularities, the growth of structure in cosmological solutions, and the theoretical basis for some recently important observational methods, such as gravitational lensing effects. There will be a broad survey of possible cosmological solutions known at present. Some topics related to particle physics and its cosmological implications will be considered. Since there are alternate theories of gravity and space-time that offer interesting features of a cosmological nature, we will also discuss some of these theories. There will be emphasis on the relationships between gravitation and other areas of theoretical physics.