Abstract
In this thesis, we first recall some basic definitions and theorems of Lie algebras and representations. In particular, we review some background on the irreducible Harish-Chandra sl(2)-modules and indecomposable sl(2)-modules. Then, we recall the definitions of Lie superalgebras and the highest weight theory for basic Lie superalgebras. Especially, we focus on some concrete examples of orthosymplectic Lie superalgebras. Furthermore, we systematically investigate the Dirac cohomology for basic Lie superalgebras. At last, we obtain the Dirac cohomology of finite-dimensional osp(1│2)-modules and the Dirac cohomology of the lowest weight osp(1│2)-modules explicitly.