Geometrical Structures in Field Theory.- 1. Grassmannians, Connections, and Integrability.- 2. The Radon-Penrose Transform.- 3. Introduction to Superalgebra.- 4. Introduction to Supergeometry.- 5. Geometric Structures of Supersymmetry and Gravitation.- Recent Developments (by Sergei A. Merkulov).- A. New Developments in Twistor Theory.- B. Geometry on Supermanifolds.- Notes.