The authors wish to thank all the mathematicians who have contributed to the ideas that are presented in these notes. The informal discussions, seminars, papers and reprints of our friends and colleagues have shaped our approach to these notes. We are indebted to our co-authors, Erik Christensen, Ken Dykema, Florin Pop, Sorin Popa, Guyan Robertson, Stuart White and Alan Wiggins, who have directly, and indirectly, inuenced us.

We wish to thank Jan Cameron, Kunal Mukherjee, Gabriel Tucci and Alan Wiggins who, while research students, read parts of the notes and made many constructive comments on them. Particular thanks go to Stuart White who read the entire manuscript, made many suggestions for improvements, and saved us from numerous errors.

Our wives Pat and Ginny have been extremely patient and understanding during the long periods that we have been immersed in this project. We have received much support and advice from Roger Astley at Cambridge University Press. Our thanks go to Robin Campbell who with great expertise turned our manuscripts and rough LATEX files into this book.

We take this opportunity to record our sincere gratitude to the National Science Foundation. Grants to the second author have enabled us to meet on numerous occasions in the last few years, allowing us to bring this book to completion.