  The fundamental theorem of arithmetic factorizes any integer into a product
of prime numbers. The Jordan-Holder theorem dissolves many groups by their
normal series which can be refined into composition series. The main topic of
this thesis is the dissociation of field extensions. We dissociate algebraic
extensions by their intermediate fields to build a tower with the greatest
possible number of Galois steps. We call "galtowerable" the extensions
admitting 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 or
infinite) admit equivalent refinements. We discuss refinement of Galois towers
to define "Galois composition towers". A field extension admits a Galois
composition tower if and only if it is finite and galtowerable. For such an
extension we obtain a Galois analogue of the Jordan-Holder theorem for groups.
Any finite group admits a normal series, but there exist finite and separable
extensions which are not galtowerable. Is it possible to pursue the dictionary
between group theory and extension theory in this case ?
