These are the proceedings of the Summer Research Conference on 4-manifolds held at Durham, New Hampshire, July 1982, under the auspices of the American Mathematical Society and National Science Foundation.

The conference was highlighted by the breakthroughs of Michael Freedman and S. K. Donaldson and by Frank Quinn's completion at the conference of the proof of the annulus conjecture. (We commend the AMS committee, particularly Julius Shaneson, who had the foresight in Spring 1981 to choose the subject, 4-manifolds, in which such remarkable activity was imminent.) Freedman and several others spoke on his work; some of their talks are represented by papers in this volume. Donaldson and Clifford H. Taubes gave surveys of their work on gauge theory and 4-manifolds and their papers are also included herein. There were a variety of other lectures, including Quinn's surprise, and a couple of problem sessions which led to the problem list.

A background of basic differential topology is adequate for potential readers.

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