The International Conference on Categorical Topology at the Free University Berlin, from the 27th of August to the 2nd of September 1978, brought together fifty mathematicians from 16 countries of the world. The meeting was organized by the editors of these proceedings. Especially, we would like to thank Priv.-Doz. Dr. Thomas Marny (scientific secretary) and Mrs. Karla Lautenschlager (congress bureau) for their assistance. We are also grateful for the help of the members of the Categorical Topology Research Group in Berlin...