In this 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 supermanifolds to the algebra-geometric approach of for example Kostant or Leites.
Alice Roger's 2007 textbook 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.
