Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. The present book is the outgrowth of lectures given at various times to students of the later undergraduate and earlier graduate years. It aims to present some of the general concepts and methods which are necessary for advanced work in algebraic geometry (as distinguished from differential geometry), but which are not now accessible to the student in any one'volume, and thus to bridge the gap between the usual text in analytic geometry and treatises or articles on special topics.