  This text is an introduction to math.AG/0110051 (to appear in Ann. Inst.
Fourier), and describes a canonical decomposition of compact K\"ahler manifolds
$X$ first by means of their "core", the unique fibration on $X$ with fibres
special, and orbifold base of general type. Being special means that there does
not exist a fibration onto an orbifold of general type. The core is next
decomposed into a tower of fibrations with all orbifold fibres either with
$\kappa=0$, or rationally generated (a weak version of rationally connected).
