This report is in two self-contained parts. The first is a collection of research problems in complex analysis. Most of the problems were posed by participants at the London Mathematical Society Symposium on Potential Theory and Conformal Mapping held at the University of Durham from 2 July to 12 July, 1976 and sponsored by the Science Research Council. The problems marked with an asterisk were posed at problem sessions held at Queen Elizabeth College, London during the academic year 1975-76. The problems are numbered consecutively with the problems in reports of two earlier symposia, references [A] and [B] below, though two additional sections, on spaces of analytic functions and on interpolation and approximation, have been added.The second part of the report is a summary of a lecture given at the symposium by Professor W. K. Hayman, reporting progress on problems in the two previous reports. The authors wish to thank Professor Hayman for his assistance in compiling this report, and the members of the symposium for suggesting so many interesting and varied problems. On behalf of all the participants we express our appreciation to the Science Research Council for its generous support. PART I: NEW PROBLEMS 1. Meromorphic Functions 1.30: Can one establish an upper bound on the number of finite asymptotic values of a meromorphic function /(z) in C, taking into account both the order of/ and the angular measure of its tracts? (W. Al Katifi) 2. Entire Functions *2.47: Let E p be the linear space of entire functions / such that for some A > 0, B > 0; K p the family of functions k(z) positive and continuous on C with exp(yl|z| p ) = o(k(z)) as \z\ -• oo, for all A > 0; S a subset of C ; and || || fc s , || || fc the semi-norms defined f o r / e £ p , keK p by k,s = sup 5^ I k(z) l\M\ II/IU = sup -c [ k(z)We say that S is a sufficient set for E p if the topologies defined by the semi-norms {|| \\ k , keK p ], {|| \\ k>s ,keK p } coincide [13].