This book presents the basic singularity theory of analytic spaces,
including local deformation theory, and the theory of plane curve
singularities. The authors develop the relevant techniques, including
Weierstraß preparation theorem, the finite coherence theorem etc., and
then discuss isolated hypersurface and plane curve singularities,
including the finite determinacy, classification of simple
singularities, topological and analytic invariants, resolution. In the
local deformation theory emphasis is placed on the issues of the
versality, obstructions, and equisingular deformations. The book
includes a thorough treatment of equisingular deformations of plane
curve singularities including a proof for the smoothness of the
mu-constant stratum based on deformations of the parametrization.