  We propose a new concept of generalized differentiation of set-valued maps
that captures the first order information. This concept encompasses the
standard notions of Frechet differentiability, strict differentiability,
calmness and Lipschitz continuity in single-valued maps, and the Aubin property
and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen
the relationship between the Aubin property and coderivatives, and study how
metric regularity and open covering can be refined to have a directional
property similar to our concept of generalized differentiation. Finally, we
discuss the relationship between the robust form of generalization
differentiation and its one sided counterpart.
