  $\mathcal{I}$-non-degenerate spaces are spacetimes that can be characterized
uniquely by their scalar curvature invariants. The ultimate goal of the current
work is to construct a basis for the scalar polynomial curvature invariants in
three dimensional Lorentzian spacetimes. In particular, we seek a minimal set
of algebraically independent scalar curvature invariants formed by the
contraction of the Riemann tensor and its covariant derivatives up to fifth
order of differentiation. We use the computer software \emph{Invar} to
calculate an overdetermined basis of scalar curvature invariants in three
dimensions. We also discuss the equivalence method and the Karlhede algorithm
for computing Cartan invariants in three dimensions.
