In [this](http://aip.scitation.org/doi/abs/10.1063/1.524585) paper about a global theory of supermanifolds, Alice Rogers develops the theory of supermanifolds as they underly supersymetric field theories from a rigorous but physicist-fiedly differential--geometric point of view from their topoligical scratch and also puts some additional structures as vector fields and tangent spaces on them. She also compares the $G^{\infty}$ or [deWitt](https://www.amazon.com/Supermanifolds-Cambridge-Monographs-Mathematical-Physics/dp/0521423775) supermanifolds to the algebra-geometric approach of for example [Konstant](http://inspirehep.net/record/105991?ln=en) or [Leites](http://iopscience.iop.org/article/10.1070/RM1980v035n01ABEH001545).

Alice Roger's 2007 [textbook](http://www.worldscientific.com/worldscibooks/10.1142/1878) explains the supermathematics needed for doing superphysics (including Grassmann algebras, super Lie groups such as the super Poincare group, etc) and contains more applications to different physics topics such as $N=1$ supersymmetry, supergravity, some aspects of string theory, or Brownian motion from the same nice differential-geometric point of view.