Introduction to supergeometry

TL;DR

This paper provides an introductory exposition of supergeometry, covering super- and graded manifolds, cohomological vector fields, graded symplectic structures, reduction, and the AKSZ formalism, aimed at newcomers and researchers in the field.

Contribution

It offers a comprehensive introduction to supergeometry concepts and techniques, including recent developments like the AKSZ formalism, in a lecture-based format.

Findings

Clarifies the structure of super- and graded manifolds

Explains the role of cohomological vector fields and graded symplectic structures

Introduces reduction techniques and the AKSZ formalism

Abstract

These notes are based on a series of lectures given by the first author at the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded manifolds, cohomological vector fields, graded symplectic structures, reduction and the AKSZ-formalism.