  In order to extract informations on pairing correlations in nuclei from
experimental mass differences, the different contributions to odd-even mass
differences are investigated within the Skyrme HFB method. In this first paper,
the description of odd nuclei within HFB is discussed since it is the key point
for the understanding of the above mentioned contributions. To go from an even
nucleus to an odd one, the advantage of a two steps process is demonstrated and
its physical content is discussed. New results concerning time-reversal
symmetry breaking in odd-nuclei are also reported.
  PACS: 21.10Dr; 21.10.Hw; 21.30.-x.
  Keywords: Mean-field theories; Pairing correlations; odd nuclei;
