What is topological data analysis?

The talk will be an introduction to topological data analysis - a field of research on the boarder of algebraic topology, statistics and computer science. The field was created to a large extent by H. Edelsbrunner, A. Zomorodian and G. Carlsson. In the first part of the talk I will describe some phenomena where this field has found applications. In the second part I will describe in some detail the construction of (various) filtered complexes, persistent homology and bar codes as well as some other constructions used in this area. In the final part I will describe a few applications in some more detail.