The goal of this book is to present local class field theory from the cohomological point of view， following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions：primarily abelian：of "local" （i.e.， complete for a discrete valuation） fields with finite residue field. For example， such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts： the first two on the general theory of local fields， the third on group cohomology. Local class field theory， strictly speaking， does not appear until the fourth part.
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