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Acknowledgments to the Second Edition

Stefan Theisen, during a period of his work on Calabi–Yau manifolds in conjunction
with string theory, brought up many questions in the summer of 1998 which lead to
a renewed interest in the subject of elliptic curves on my part.
Otto Forster gave a course in Munich during 2000–2001 on or related to elliptic
curves. We had discussions on the subject leading to improvements in the second
edition, and at the same time he introduced me to the role of elliptic curves in cryp-
tography.
A reader provided by the publisher made systematic and very useful remarks on
everything including mathematical content, exposition, and English throughout the
manuscript.
Richard Taylor read a first version of Chapter 18, and his comments were of
great use. F. Oort and Don Zagier offered many useful suggestions for improvement
of parts of the first edition. In particular the theory of elliptic curves over the real
numbers was explained to me by Don.
With the third appendix T. Bauer, M. Joachim, and S. Schwede offered many
useful suggestions.
During this period of work on the second edition, I was a research professor
from Haverford College, a visitor at the Max Planck Institute for Mathematics in
Bonn, a member of the Graduate College and mathematics department in Munich,
and a member of the Graduate College in M¨ unster. All of these connections played
a significant role in bringing this project to a conclusion.

Max-Planck-Institut f¨ ur Mathematik Dale Husem¨ oller
Bonn, Germany