The study of geometry can play an important role in stimulating mathematical imagination and intuition, particularly in its relation to algebra. The author of this book is convinced that the two are but different sides of the same coin, and that they should be presented together to a student of mathematics as soon as the curriculum will permit. Certainly, no graduate of an Honours course should miss at least a brief exposure to these stimulating ideas.

When the first edition of this book appeared, a reviewer in the American Mathematical Monthly commented: ‘If this book had a subtitle, it might well have been “The Theorems of Desargues and Pappus,” for these two theorems play a central role throughout the text; their dependence and independence of various axioms is continually studied. Nowhere before, in English, has the importance of these two theorems been so carefully demonstrated…this is a most excellent book, and it will inspire many students of mathematics.’

Largely as a result of the work of Ruth Moufang, the interplay between algebraic and geometrical ideas has been further investigated of recent years. Many interesting problems have come to light, some of which have been solved. In this fourth edition, an Appendix has been added which attempts to summarize a part of this work and provide the reader with references so that he may learn more of these interesting developments.

Gilbert de B. Robinson was born in Toronto, and graduated from the University of Toronto in 1927. He received his Ph.D. from Cambridge University in 1931. He has been a member of the staff on the Department of Mathematics at the University of Toronto from 1931 to the present. He was Visiting Professor at Michigan State University in 1953-54. From 1940 to 1945 Professor Robinson served with the National Research Council in Ottawa; he was honoured with the M.B.E in 1946.

Professor Robinson is a Fellow of the Royal Society of Canada, and was President of Section II in 1959-60, 1961-62. From 1933 to 1957, he was President of the Canadian Mathematical Congress. He has taken an active part in the founding and development of the Canadian Journal of Mathematics.

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