PREFACE This manuscript is a detailed presentation of the ten lectures given by the author at the Conference Board of Mathematical Sciences Regional Conference on Three-Manifold Topology, held October 8-12, 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to present the current state of affairs in three-manifold topology and to integrate the classical results with the many recent ad- vances and new directions. The ten principal lectures presented here deal with the study of three-manifolds via incompressible surfaces. At the conference, these lec- tures were supplemented by eight special lectures: two lectures each by Professor Joan Birman of Columbia University (Heegaard Theory), Professor Sylvain Cappell of the Courant Institute (branched coverings and applica- tions to 4-dimensional topology), Professor Robion Kirby of The University of California/Berkeley (three-dimensional knot theory) and Professor William Thurston of Princeton University (three-dimensional hyperbolic geo- metry) . I wish to thank the host university, the members of the Department of Mathematics at V.P.I. & S.U., and the Conference Director, Professor Charles Feustel. A special thanks to the Conference Coordinator, Professor Ezra f BudT Brown. I believe that the conference was a success and that much of the success was due to the special lectures given by the previously named parti- cipants. I wish to acknowledge my thanks to Professors Birman, Cappell, Kirby and Thurston. v
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