This is an introductory text for a first course in algebraic topology. The authors present the beginning material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This point of view clearly has applications in algebraic geometry as understood by Lawson and Voevodsky. This carefully written book can be read by any student who knows some topology. It will be a useful place to quickly learn this novel homotoy-theoretic point of view of algebraic topology.

From the reviews:"This is a basic course on algebraic topology and it is excellently written and composed and can be strongly recommended to anybody wishing to learn the field. The reader can find many examples, calculations, and also a number of exercises. The book has two appendices, references consisting of 83 items and a long list of symbols. There are many remarks and comments making the orientation of the reader in the field of algebraic topology easier ." (EMS, June, 2004)"The modus operandi of algebraic topology is to associate algebraic invariants, such as groups or rings, to a topological space in such a way that equivalent spaces exhibit isomorphic invariants; here, 'equivalent' may be chosen to fit the geometry of the problem. In this book, 'equivalent' means homotopy equivalent . For its clarity and directness, a welcome addition to advanced mathematics collections. Upper-division undergraduates through faculty." (J. McCleary, CHOICE, December, 2002)"The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory . The basic concepts of homotopy theory are used to construct singular homology and cohomology, as well as K-theory. Throughout the text many other fundamental concepts are introduced ." (L'Enseignement Mathematique, Vol. 48 (3-4), 2002)The book of Aguilar, Gitler and Prieto gives an interesting new approach for a first course in algebraic topology. What is also very interesting is the fact that the book contains a detailed presentation of some deep results of algebraic topology not usually covered by a first book in algebraic topology . The text is carefully well written. the student in algebraic topology will find in the book a lot of interesting well-exposed material. (Yves Félix, Bulletin of the Belgian Mathematical Society, 2007)

Inhalt
Function Spaces.- Connectedness and Algebraic Invariants.- Homotopy groups.- Homotopy Extension and Lifting Properties.- CW-Complexes and Homology.- Homotopy Properties of CW-Complexes.- Cohomology Groups and Related Topics.- Vector Bundles.- K-Theory.- Adams Operations and Applications.- Relations Between Cohomology and Vector Bundles.- Cohomology Theories and Brown Representability.