In September 1964 a N. A. T. O. advanced study institute was held at Imperial College, London University. Arising out of this a book of problems with the above title was collected by me and published by the Athlone Press in 1967. It is my aim in this article to report on the progress that has been made on the problems of this book in so far as I am aware of it. I have given the references that I could easily trace. However, much of the work is as yet unpublished. Some of the solutions were first announced at the present conference in Canterbury. After discussing progress on the old problems I shall describe some new problems which were contributed by members of this conference.

In addition to the above problem collection the attention of the reader should also be drawn to the recent collection of Ch. Pommerenke.

I acknowledge with gratitude the very considerable help I have had from Professor Clunie, particularly in the tracing of references.

Progress on the previous problems

The problems are numbered as in the book referred to in the introduction [P], The notation and terminology of that book will be used throughout.

Meromorphic functions

This problem has now been completely settled by Drasin in a result first announced at the Canterbury conference. An abstract appears elsewhere in these proceedings.