  Theory for open curves over a local field. After introducing the reciprocity
map, we determine the kernel and the cokernel of this map. In addition to this,
the Pontrjagin dual of the reciprocity map is also investigated. This gives the
one to one correspondence between the set of finite abelian \'etale coverings
and the set of finite index open subgroups of the id\`ele class group as in the
classical class field theory under some assumptions.
