I. G. Farben is a shortened version of the name Interessen Gemeinshaft Farbenindustrie which means " Community of Interest of the Dye Industry." It began as a trade association and developed more and more unified operations. Eventually, the seven companies involved joined into a single corporate unit known as I. G. Farbenindustrie, A. G. in 1925. The A. G. stands for Aktiengesellschaft, which translates to "sharecompany." Now you see why it is usually shortened to I. G. Farben.
From Frank A. Howard, Buna Rubber: The Birth of an Industry. New York: D. van Nostrand Company, Inc., 1947.