  This is a chapter for a planned collective volume entitled "New spaces in
mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a
short formal exposition of supergeometry as it is understood by mathematicians.
The second part discusses aspects of supergeometry that are used by physicists
in relation to supersymmetry. Finally, the third part is an attempt to uncover
homotopy-theoretic roots of the super formalism.
