A classic available again! This book traces the history of algebraic topology beginning with its creation by Henry Poincaré in 1900, and describing in detail the important ideas introduced in the theory before 1960. In its first thirty years the field seemed limited to applications in algebraic geometry, but this changed dramatically in the 1930s with the creation of differential topology by Georges De Rham and Elie Cartan and of homotopy theory by Witold Hurewicz and Heinz Hopf. The influence of topology began to spread to more and more branches as it gradually took on a central place in mathematics. Written by a world-renowned mathematician, this book will make exciting reading for anyone working with topology.