[en] A description is given of the principles and the main facilities of SIGMA (System for Interactive Graphical Mathematical Applications), a programming language for scientific computing whose major characteristics are: automatic handling of multi-dimensional rectangular arrays as basic data units, interactive operation of the system, and graphical display facilities. After introducing the basic concepts and features of the language, it describes in some detail the methods and operators for the automatic handling of arrays and for their graphical display, the procedures for construction of programs by users, and other facilities of the system. The report is a new version of CERN 73-5. (Auth.)