Based on a series of lectures given at Sheffield during 1971-72, this text is designed to introduce the student to homological algebra avoiding the elaborate machinery usually associated with the subject. This book presents a number of important topics and develops the necessary tools to handle them on an ad hoc basis. The final chapter contains some previously unpublished material and will provide additional interest both for the keen student and his tutor. Some easily proven results and demonstrations are left as exercises for the reader and additional exercises are included to expand the main themes. Solutions are provided to all of these. A short bibliography provides references to other publications in which the reader may follow up the subjects treated in the book. Graduate students will find this an invaluable course text as will those undergraduates who come to this subject in their final year.