  The aim of this text is to present the concept of systole of a compact
riemannian manifold and to give an overview of systolic geometry. I will also
present the "regularization technique", which leads to major results in
systolic geometry. I will detail how this technique allows to link the systolic
volume of some closed riemannian manifolds to homotopical invariants of these
manifolds, such as the Betti numbers (according to Gromov) and the minimal
entropy (according to Sabourau).
