"Algebraic topoligy books that emphasize geometrical intuition usually have only a modest technical reach. Remarkably, Hatcher (Cornell Univ.) offers a highly geometrical treatment that neverheless matches the coverage of, e.g., Edwin Henry Spanier's very formidable and identically titled classic work... He promises two advanced companion volumes, one on spectral sequences, one on vector bundles. One anticipates the combined treatise doing for algebraic topology what Michael Spivak's magisterial five-volume set did for differential geometry." Choice
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. A unique feature of the book is the inclusion of many optional topics for which elementary expositions are hard to find. Researchers and students alike will welcome this aspect of the book.