Charles Loewner, Professor of Mathematics at Stanford University from 1950 until his death in 1968, was a Visiting Professor at the University of California at Berkeley on five separate occasions. During his 1955 visit to Berkeley he gave a course on continuous groups, and his lectures were reproduced in the form of mimeographed notes. Loewner planned to write a detailed book on continuous groups based on these lecture notes, but the project was still in the formative stage at the time of his death. Since the notes themselves have been out of print for several years, Professor Harley Flanders, Department of Mathematics, Tel-Aviv University, and Professor Murray H. Protter, Department of Mathematics, University of California, Berkeley, have taken this opportunity to revise and correct the original fourteen lectures and make them available in permanent form.
Loewner became interested in continuous groups—particularly with respect to possible applications in geometry and analysis—when he studied the three-volume work on transformation groups by Sophus Lie. He managed to reconstruct a coherent development of the subject by synthesizing Lie's numerous illustrative examples, many of which appeared only as footnotes. The examples contained in this book are primarily geometric in character and reflect the unique way in which Loewner viewed each of the topics he treated.
This book is part of a new series, Mathematicians of Our Time, edited by Professor Gian-Carlo Rota, Department of Mathematics, Massachusetts Institute of Technology. The series will also include the collected and previously published papers of Charles Loewner.