  We propose a unifying general (i.e. not assuming the mapping to have any
particular structure) view on the theory of regularity and clarify the
relationships between the existing primal and dual quantitative sufficient and
necessary conditions including their hierarchy. We expose the typical sequence
of regularity assertions, often hidden in the proofs, and the roles of the
assumptions involved in the assertions, in particular, on the underlying space:
general metric, normed, Banach or Asplund. As a consequence, we formulate
primal and dual conditions for the stability properties of solution mappings to
inclusions
