  We obtain all the three-dimensional Lorentzian metrics which admit three
Killing vectors. The classification has been done with the aid of the formalism
which exploits the obstruction criteria for the Killing equations recently
developed by present authors. The current classification method does not rely
on the transitivity property of the isometry group. It turns out that the
Lorentzian manifold harbors a much richer spectrum of metrics with various
Segre types, compared to the Riemannian case.
