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In this note we continue the study, initiated in [1], of the class S*(α) of functions(1.1)that are analytic and univalent in the unit disc U and satisfy the condition(1.2)S*(1) is the frequently studied class of univalent star-like functions. For each α, S*(α) is a subclass of the class K(α) of close-to-convex functions of order α introduced by Pommerenke [4]. Properties of the class S*(α) proved useful in studying the coefficient behaviour of bounded univalent functions that are analytic and map U onto a convex domain [1]. In this note we investigate the problem of determiningbut we are able to give only a partial solution.

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This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.

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].

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