The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate or beginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is toward homotopy theory with a geometric point of view. This book would provide a more than adequate background for a standard algebraic topology course that begins with homology theory. For more information see www.bangor.ac.uk/r.brown/topgpds.html This version dated April 19, 2006, has a number of corrections made.