  A number of scalar invariant characterizations of the Kerr solution are
presented. These characterizations come in the form of {\em quality factors}
defined in stationary space-times. A quality factor is a scalar quantity
varying in the interval $[0,1]$ with the value 1 being attained if and only if
the space-time is locally isometric to the Kerr solution. No knowledge of the
Kerr solution is required to compute these quality factors. A number of
different possibilities arise depending on whether the space-time is Ricci-flat
and asymptotically flat, just Ricci-flat, or Ricci non-flat. In each situation
a number of quality factors are constructed and analysed. The relevance of
these quality factors is clear in any situation where one seeks a rigorous
formulation of the statement that a space-time is "close" to the Kerr solution,
such as: its non-linear stability problem, the asymptotic settlement of a
radiating isolated system undergoing gravitational collapse, or in the
formulation of some uniqueness results.
