This book is a clear exposition, with exercises, of the basic ideas of algebraic topology: homology (singular, cellular and simplicial), homotopy groups, and cohomology rings. It is suitable for a two semester course at the beginning graduate level, requiring as prerequisites a knowledge of point set topology, and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of new abstract concepts as they are introduced, making this book of great value to the student. Es handelt sich um eine didaktisch orientierte Einführung in die algebraische Topologie.