Includes bibliographical references.

Multidimensional complete fields: Topology and other basic constructions;A ramification filtration of the Galois group of a local field;Class field theory for multidimensional complete fields with quasifinite residue fields;On adic representations arising from formal groups;The pairing on groups in fields of valuation of rank Artin-Hasse exponentials and Bernoulli numbers;Some approaches to the construction of abelian extensions for mathfrak {p} adic fields;Structure theorems for complete fields;Unit fractions;Collections of multiple sums;On convergence of series over local fields;On K�ock's conjecture about shuffle products