  The lectures are devoted to a complete exposition of the theory of
singularities of the Navier Stokes equations solution studied by Leray, in a
simple geometrical setting in which the fluid is enclosed in a container $\O$
with periodic boundary conditions and side size $L$. The theory is due to the
work of Scheffer, Caffarelli, Kohn, Nirenberg and is called here CKN-theory as
it is inspired by the work of the last three authors which considerably
improved the earlier estimates of Scheffer.
