This classic text appears here in a new edition for the first time in four decades.The new edition, with the aid of two new authors, brings it up to date for a new generation of mathematicians and mathematics students. Elements of Algebraic Topology provides the most concrete approach to the subject.With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for communicating complex topics and the fun nature of algebraic topology for beginners. This second edition retains the essential features of the original book.Most of the notation and terminology are the same. There are some useful additions. There is a new introduction to homotopy theory. A new Index of Notation is included. Many new exercises are added. Algebraic topology is a cornerstone of modern mathematics.Every working mathematician should have at least an acquaintance with the subject.This book, which is based largely on the theory of triangulations, provides such an introduction.It should be accessible to a broad cross-section of the profession—both students and senior mathematicians.Students should have some familiarity with general topology.