  Modules over affine Lie superalgebras ${\cal G}$ are studied, in particular,
for ${\cal G}=\hat{OSP(1,2)}$. It is shown that on studying Verma modules, much
of the results in Kac-Moody algebra can be generalized to the super case. Of
most importance are the generalized Kac-Kazhdan formula and the
Malikov-Feigin-Fuchs construction, which give the weights and the explicit form
of the singular vectors in the Verma module over affine Kac-Moody
superalgebras. We have also considered the decomposition of the admissible
representation of $\hat{OSP(1,2)}$ into that of $\hat{SL(2)}\otimes$Virasoro
algebra, through which we get the modular transformations on the torus and the
fusion rules. Different boundary conditions on the torus correspond to the
different modings of the current superalgebra and characters or
super-characters, which might be relevant to the Hamiltonian reduction
resulting in Neveu-Schwarz or Ramond superconformal algebras. Finally, the
Felder BRST complex, which consists of Wakimoto modules by the free field
realization, is constructed.
