This reading course studies nilpotent orbits of reductive Lie algebras aiming at application to unitary representations of reductive Lie groups by the orbit method. It is based on the fundamental theory of nilpotent orbits and focused on algebraic and geometric aspects of the sheets of reductive Lie algebras, singularities of closures of nilpotent orbits and Slodowy slices. Students should seek the course instructor's approval to take this course.