This volume mainly focuses on various comprehensive topological theories, with the exception of a paper on combinatorial topology versus point-set topology by I.M. James and a paper on the history of the normal Moore space problem by P. Nyikos. The history of the following theories is given: pointfree topology, locale and frame theory (P. Johnstone), non-symmetric distances in topology (H.-P. Kunzi), categorical topology and topological constructs (E. Lowen-Colebunders and B. Lowen), topological groups (M. G. Tkacenko) and finally shape theory (S. Marde J. Segal). Together with the first two volumes, this work focuses on the history of topology, in all its aspects. It presents views and insights into the problems and development of topological theories and applications of topological concepts, and into the life and work of topologists. It aims to encourage not only further study in the history of the subject, but also further mathematical research in the field.