People have been interested in knots at least since the time of Alexander the Great and his encounter with the Gordian knot. There are famous knot illustrations in the Book of Kells and throughout traditional Islamic art. Lord Kelvin believed that atoms were knots in the ether and he encouraged Tait to compile a talbe of knots about 100 years ago. In recent years, the Jones polynomial has stimulated much interest in possible relationships between knot theory and physics. The book is concerned with the fundamental question of the classification of knots, and more generally the classification of arbitrary (compact) topological objects which can occur in our normal space of physical reality. Professor Hemion explains his classification algorithm - using the method of normal surfaces - in a simple and concise way. The reader is thus shown the relevance of such traditional mathematical objects as the Klein bottle or the hyperbolic plane to this basic classification theory. The Classification of Knots and 3-dimensional Spaces will be of interest to mathematicians, physicists, and other scientists who want to apply this basic classification algorithm to their research in knot theory.