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The fundamental theorem of arithmetic factorizes any integer into a productof prime numbers. The Jordan-Holder theorem dissolves many groups by theirnormal series which can be refined into composition series. The main topic ofthis thesis is the dissociation of field extensions. We dissociate algebraicextensions by their intermediate fields to build a tower with the greatestpossible number of Galois steps. We call "galtowerable" the extensionsadmitting a field tower all the steps of which are Galois extensions,i.e. a"Galois tower". Two Galois towers of the same galtowerable extension (finite orinfinite) admit equivalent refinements. We discuss refinement of Galois towersto define "Galois composition towers". A field extension admits a Galoiscomposition tower if and only if it is finite and galtowerable. For such anextension we obtain a Galois analogue of the Jordan-Holder theorem for groups.Any finite group admits a normal series, but there exist finite and separableextensions which are not galtowerable. Is it possible to pursue the dictionarybetween group theory and extension theory in this case ?

Dissociation des Extensions Algebriques de Corps par les Extensions Galoisiennes ou Galsimples non Galoisiennes