In the last two decades, with the ever higher increasing amount of data of many kinds and, usually, of high dimension, it has revealed meaningfull to be able to extract new and additional infomation from data, overall if it is related to intrinsic properties of themselfes. It has motivated the birth of a new field of research, the so called Topological Data Analysis. Thanks to the strong theoretical basis of algerabraic topology, it allows to extract qualitative information from dataset, as point clouds, images, graphs, time series, ecc…, related to the “shape of data”, and to use them into machine learning and deep learning frameworks. 

In this talk, first we will introduce the main tool of TDA called persistent homology with basic definitions and notions. Then, after the introduction of the classification problem, we will discuss how to use the new topological information in such a context.