  This paper is submitted to Algebraic-Number-Theory Archives for validation by
Number Theorists Community. It is an update of the previous versions ANT-0155,
ANT-0170, ANT-0205, ANT-0237, ANT-0321, ANT-0333, and ANT-0356, of which the
first four were titled `A generalization of Eichler criterium for Fermat's Last
Theorem' and the last three were titled `A classical approach on Fermat-Wiles
theorem'.
  This version contains a complete reorganization of the paper with a first
part dealing with cyclotomic fields (independently of FLT) from page 10 to 72
and a second part dealing with FLT from page 73 to end.
  This version improves our previous results on cyclotomic fields and contains
several significant error corrections.
  The proofs rest on classical theory of cyclotomic number fields $\Q(zeta_p)$.
