This course will build upon PHYS 5240 and will explore topics in relativity that are frequently used in research in gravitation and cosmology theory. This will include Hamiltonian, tetrad, and Landau-Lifshitz formulations of relativity; perturbations of flat spacetime, black holes, and compact stars; conformal methods, singularity theorems, and black-hole mechanics; and inflation and cosmological perturbation theory.