This text is an introduction to topology and homotopy. Topics are integrated into a coherent whole and developed slowly so students will not be overwhelmed. The first half of the text treats the topology of complete metric spaces, including their hyperspaces of sequentially compact subspaces. The second half of the text develops the homotopy category. There are numerous examples and over 900 exercises, representing a wide range of difficulty. This book should be of interest to undergraduates and researchers in mathematics.