The Geometry of Supermanifolds

I: Foundations.- I - Elements of graded algebra.- 1. Graded algebraic structures.- 2. Graded algebras and graded tensor calculus.- 3. Matrices.- II - Sheaves and cohomology.- 1. Presheaves and sheaves.- 2. Sheaf cohomology.- 3. de Rham, Dolbeault, and ?ech cohomologies.- 4. Graded Ringed spaces.- II Supermanifolds.- III - Categories of supermanifolds.- 1. Graded manifolds.- 2. Supersmooth functions.- 3. GH? functions.- 4. G-supermanifolds.- IV - Basic geometry of G-supermanifolds.- 1. Morphisms.- 2. Products.- 3. Super vector bundles.- 4. Graded exterior differential calculus.- 5. Projectable graded vector fields.- 6. DeWitt supermanifolds.- 7. Rothstein's axiomatics.- V - Cohomology of supermanifolds.- 1. de Rham cohomology of graded manifolds.- 2. Cohomology of graded differential forms.- 3. Cohomology of DeWitt supermanifolds.- 4. Again on the structure of DeWitt supermanifolds.- VI - Geometry of super vector bundles.- 1. Connections.- 2. Super line bundles.- 3. Characteristic classes.- 4. Characteristic classes in terms of curvature forms.- VII - Lie supergroups and principal super fibre bundles.- 1. Lie supergroups.- 2. Lie supergroup actions.- 3. Principal superfibre bundles.- 4. Connections.- 5. Associated super fibre bundles.