  TDA (topological data analysis) is a relatively new area of research related
to importing classical ideas from topology into the realm of data analysis.
Under the umbrella term TDA, there falls, in particular, the notion of
persistent homology, which can be described in a nutshell, as the study of
scale dependent homological invariants of datasets.
  In these notes, we provide a terse self contained description of the main
ideas behind the construction of persistent homology as an invariant feature of
datasets, and its stability to perturbations.
