  In recent papers, Fesenko has defined the non-abelian local reciprocity map
for every totally-ramified arithmetically profinite ($APF$) Galois extension of
a given local field $K$ by extending the works of Hazewinkel and
Neukirch-Iwasawa. The theory of Fesenko extends the previous non-abelian
generalizations of local class field theory given by Koch-de Shalit and by A.
Gurevich. In this paper, which is research-expository in nature, we give a
detailed account of Fesenko's work including all the skipped proofs.
