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Acknowledgments to the First Edition

Being an amateur in the field of elliptic curves, I would have never completed a
project like this without the professional and moral support of a great number of per-
sons and institutions over the long period during which this book was being written.
John Tate’s treatment of an advanced subject, the arithmetic of elliptic curves,
in an undergraduate context has been an inspiration for me during the last 25 years
while at Haverford. The general outline of the project, together with many of the
details of the exposition, owe so much to Tate’s generous help.
The E.N.S. course by J.-P. Serre of four lectures in June 1970 together with two
Haverford lectures on elliptic curves were very important in the early development
of the manuscript. I wish to thank him also for many stimulating discussions. El-
liptic curves were in the air during the summer seasons at the I.H.E.S. around the
early 1970s. I wish to thank P. Deligne, N. Katz, S. Lichtenbaum, and B. Mazur for
many helpful conversations during that period. It was the Haverford College Faculty
Research Fund that supported many times my stays at the I.H.E.S.
During the year 1974–5, the summer of 1976, the year 1981–2, and the spring
of 1986, I was a guest of the Bonn Mathematics Department SFB and later the Max
Planck Institute. I wish to thank Professor F. Hirzebruch for making possible time
to work in a stimulating atmosphere and for his encouragement in this work. An
early version of the first half of the book was the result of a Bonn lecture series on
Elliptische Kurven. During these periods, I profited frequently from discussions with
G. Harder and A. Ogg.
Conversations with B. Gross were especially important for realizing the final
form of the manuscript during the early 1980s. I am very thankful for his encourage-
ment and help. In the spring of 1983 some of the early chapters of the book were used
by K. Rubin in the Princeton Junior Seminar, and I thank him for several useful sug-
gestions. During the same time, J. Coates invited me to an Oberwolfach conference
on elliptic curves where the final form of the manuscript evolved.
During the final stages of the manuscript, both R. Greenberg and R. Rosen read
through the later chapters, and I am grateful for their comments. I would like to
thank P. Landweber for a very careful reading of the manuscript and many useful
comments.