The project is concerned with several aspects of Lie superalgebras. This is an extension of the concept of Lie algebras and is motivated by theoretical physics. The first aspect is homological algebra, more ceoncretely Bernstein-Gelfand-Gelfand resolutions, Kostant cohomology and Bott-Borel-Weil theory. The second aspect is the classification of the primitive ideals in the universal enveloping algebra of the lie superalgebra.