An introduction to supermanifolds and supersymmetry

The aim of these notes (which were partially covered in lectures given at the Peyresq Summer School on 17–22 June, 2002) is to give an introduction to some mathematical aspects of supersymmetry. Some (hopefully) original point of view are added, by using and developing some results in arXiv:math-ph/0603045, where maps of supermanifolds are analyzed in details and, also, in the presentation of the super Minkowski spaces in dimensions 3, 4, 6 and 10.