SUMMARY: 
We emphasize several faces of the critical phenomena for maps between two
manifolds Mm and Nn. In the nite dimensional setting, it basically concerns
those points of the source manifold where the rank of the dierential is
strictly less than its maximum possible value minfm; ng. Note that for n = 1
the critical points are those where the dierential vanishes and this fact is
being considered as the denition of the critical points of real valued functions
dened on innite dimensional Banach spaces. The set of images of such points
is also part of the critical phenomena and the size of the critical sets and the
sets of critical values is sometimes evaluated. 
