Supermanifolds and Supergroups [electronic resource] : Basic Theory / by Gijs M. Tuynman.

$$ \mathfrak{A} $$ -graded commutative linear algebra -- Linear algebra of free graded A-modules -- Smooth functions and A-manifolds -- Bundles -- The tangent space -- A-Lie groups -- Connections.

Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections. The book requires standard undergraduate knowledge on super differential geometry and super Lie groups.