[en] 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.

Center for Mathematical Analysis, Geometry and Dynamical Systems, IST Lisbon (Lisbon, Portugal)

Swiss National Science Foundation (SNF-grants 20-113439 and 20-131813) ; FCT/POCTI/FEDER through project PTDC/MAT/098936/2008 ; Center for Mathematical Analysis, Geometry and Dynamical Systems, IST Lisbon (Lisbon, Portugal)