Going back to work by Edelsbrunner, Carlsson and others in computational as well as "applied" topology, the field of Topological Data Analysis (TDA) is by now widely established. It provides a toolbox that is already getting applied to various fields outside mathematics, in particular to the life sciences. Assuming no prior knowledge about topology, we will begin by pointing to examples of how a very classical invariant, homology, can be applied (outside math) as well as computed in practice. We will then see how applying homology to growing $\epsilon$-neighborhoods of point cloud data in $\mathbb{R}^n$ leads to a multiscale data descriptor, called the barcode. If time permits we mention some representation theoretic perspectives on this.
