This book was written to be a readable introduction to Algebraic Topology with rather broad coverage of the subject. Our viewpoint is quite classical in spirit, and stays largely within the conﬁnes of pure Algebraic Topology. In a sense, the book could have been written thirty years ago since virtually all its content is at least thatold. However, the passage of the intervening years has helped clarify what the most important results and techniques are. For example, CW complexes have proved over time to be the most natural class of spaces for Algebraic Topology, so they are emphasized here much more than in the books of an earlier generation. This emphasisalso illustrates the book’s general slant towards geometric, rather than algebraic, aspects of the subject. The geometry of Algebraic Topology is so pretty, it would seem a pity to slight it and to miss all the intuition that it provides. At deeper levels, algebra becomes increasingly important, so for the sake of balance it seems only fair to emphasize geometry at the beginning.