  We present an algebraic procedure that finds the Lie algebra of the local
Killing fields of a smooth metric. In particular, we determine the number of
independent local Killing fields about a given point on the manifold. Spaces of
constant curvature and locally symmetric spaces are also discussed.
Furthermore, we obtain a complete classification of the Lie algebra of local
Killing fields for surfaces in terms of conditions upon the Gauss curvature.
