  Let F be a non-archimedean local field. We establish the local Langlands
correspondence for all inner forms of the group $SL_n (F)$. It takes the form
of a bijection between, on the one hand, conjugacy classes of Langlands
parameters for $SL_n (F)$ enhanced with an irreducible representation of an
S-group and, on the other hand, the union of the spaces of irreducible
admissible representations of all inner forms of $SL_n (F)$. An analogous
result is shown in the archimedean case.
  To settle the case where F has positive characteristic, we employ the method
of close fields. We prove that this method is compatible with the local
Langlands correspondence for inner forms of $GL_n (F)$, when the fields are
close enough compared to the depth of the representations.
