>         Can somebody explain me why the crystal used in PIC's must be
> with parallel resonant frequency ?
>
>         Which would be the result is I use a crystal with series
> resonance ?
>
>         Which is the difference ?

The difference, from what I understand, is usually just this: one type of
oscillator will run a little faster than the crystals fundamental; the other
will run a little slower than the fundamental [I think parallel is faster
but I'm not sure--the following may be backwards].  Ergo, to get a 1,000,000
Hz oscillator in a series resonant circuit you need about a 1,003,000Hz
crystal and to get 1,000,000Hz in a parallel circuit you need a 997,000Hz
crystal.  Note that both of the above crystals would be called 1,000,000Hz
since that's the "intended" oscillation speed, but using a series crystal in
a parallel circuit would result in an oscillator that ran about 0.6% fast.

NOTE: This is reproduced from memory from a magazine Q&A I saw ages ago and
may bear no resemblance to reality--use at your own risk.