3-manifolds
John Hempel
Princeton University Press
For many years, John Hempel's book has been a standard text on   the topology of 3-manifolds. Even though the field has grown   tremendously during that time, the book remains one of the best   and most popular introductions to the subject.    <P>The theme of this book is the role of the fundamental group in   determining the topology of a given 3-manifold. The essential   ideas and techniques are covered in the first part of the book:   Heegaard splittings, connected sums, the loop and sphere   theorems, incompressible surfaces, free groups, and so on. Along   the way, many useful and insightful results are proved, usually   in full detail. Later chapters address more advanced topics,   including Waldhausen's theorem on a class of 3-manifolds that is   completely determined by its fundamental group. The book   concludes with a list of problems that were unsolved at the time   of publication.    <P>Hempel's book remains an ideal text to learn about the world of   3-manifolds. The prerequisites are few and are typical of a   beginning graduate student. Exercises occur throughout the text.    <P>Other key books on low-dimensional topology available from the   AMS are Knots and Links, Lectures on Three-Manifold Topology,   and The Knot Book.