  The paper is devoted to the development of a comprehensive calculus for
directional limiting normal cones, subdifferentials and coderivatives in finite
dimensions. This calculus encompasses the whole range of the standard
generalized differential calculus for (non-directional) limiting notions and
relies on very weak (non-restrictive) qualification conditions having also a
directional character. The derived rules facilitate the application of tools
exploiting the directional limiting notions to difficult problems of
variational analysis including, for instance, various stability and sensitivity
issues. This is illustrated by some selected applications in the last part of
the paper.
