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In the past decade the language and methods ofmodern differential
geometry have been increasingly used in theoretical physics. What
seemed extravagant when this book first appeared 12 years ago, as
lecture notes, is now a commonplace. This fact has strengthened my
belief that today students of theoretical physics have to learn
that language-and the sooner the better. Afterall, they willbe the
professors ofthe twenty-first century and it would be absurd if
they were to teach then the mathematics of the nineteenth century.
Thus for this new edition I did not change the mathematical
language. Apart from correcting some mistakes I have only added a
section on gauge theories. In the last decade it has become evident
that these theories describe fundamental interactions, and on the
classical level their structure is suffi cientlyclear to qualify
them for the minimum amount ofknowledge required by a theoretician.
It is with much regret that I had to refrain from in corporating
the interesting developments in Kaluza-Klein theories and in
cosmology, but I felt bound to my promise not to burden the
students with theoretical speculations for which there is no
experimental evidence. I am indebted to many people for suggestions
concerning this volume. In particular, P. Aichelburg, H. Rumpf and
H. Urbantke have contributed generously to corrections and
improvements. Finally, I would like to thank Dr. 1. Dahl-Jensen for
redoing some of the figures on the computer."
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