The target in this paper, is to extend an L-topological group to a complete L-topological
group, and so giving the notion of the completion of an L-topological group. In the way, we have
introduced the notion of the completion of an L-uniform space.
Keywords: L-topological groups; complete L-topological groups; L-uniform spaces; complete L-
uniform spaces; U-cauchy filters; L-filters; L-topological spaces.