algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety singularities of mappings; Thom-Mather theory; nice dimensions; right-left equivalence; contact equivalence; stability; versal unfoldings; finite determinacy; vector fields and flows; local conical structure; Thom-Boardman singularities; topological stability; unstable map-germs; unipotent algebraic groups; critical space; discriminants; bifurcation sets; isosingular locus; logarithmic tangent space; logarithmic transversality; stable perturbations; disentanglement of a map; image Milnor numbers; discriminant Milnor numbers; free and almost free divisors; complete intersections; Fitting ideals; conductor ideals; multiple point spaces; knot theory; Reidemeister moves; rank condition; parameterised hypersurfaces; maximal Cohen-Macaulay modules; duality; Gorenstein rings; canonical module; triple points 