  Topological Data Analysis (TDA) is a novel, and relatively new approach to
analysing high-dimensional data sets. It does this by focussing on global
properties like the shape and connectivity of the data giving it a significant
advantage over more conventional tools based on cluster analysis, a localised
property of the data. However, some of its mathematical foundations, like
algebraic topology and discrete Morse theory, are perceived as an
intimidatingly steep upramp into the subject. Consequently, it has enjoyed much
less popularity as a data-analysis tool than less abstract methods. This
article aims to change this. By focusing on a small set of simple examples,
chosen primarily for their pedagogical value, we introduce and explain TDA's
two principle branches; persistent homology and the Mapper algorithm. We then
illustrate the universality of the method by discussing its application to the
intriguing data set of fast radio burst (FRB) observations. We close the
article with a discussion of the resilience of topological data analysis to
noise and some statistical and computational challenges faced by the method.
