  This is an invited contribution to the 2nd edition of the Encyclopedia of
Mathematical Physics, that provides a very short survey of derived symplectic
geometry.
  Derived symplectic geometry studies symplectic structures on derived stacks.
Derived stacks are the main players in derived geometry, the purpose of which
is to deal with singular spaces, while symplectic structures are an essential
ingredient of the geometric formalism of classical mechanics and classical
field theory. In addition to providing an overview of a relatively young field
of research, we provide a case study on Casson's invariant.
