1980 Etale Cohomology

Princeton Mathematical Series 33, Princeton University Press, 323+xiii pages, ISBN 0-691-08238-3
An exposition of étale cohomology assuming only a knowledge of basic scheme theory.
In print. List price 125 USD. PUP, An online bookstore
Sales as of June 30, 2012: 4006. MR citations since 1997: 640.

Notes for a revised expanded version.   1. Etale Morphisms 11.10.12 2. Sheaf Theory NA 3. Cohomology NA 4. The Brauer Group NA 5. The Cohomology of Curves and Surfaces NA 6. The Fundamental Theorems NA A. Limits NA B. Spectral Sequences NA C. Hypercohomology NA D. Derived Categories 31.03.13

In the 1970s, derived categories were still quite new, and known to only a few algebraic geometers, and so I avoided using them. In some places this worked out quite well, for example, contrary to statements in the literature they are not really needed for the Lefschetz trace formula with coefficients in Z/mZ, but in others it led to complications. Anyone who doubts the need for derived categories should try studying the Kunneth formula (VI, 8) without them. In the new version, I shall use them. I also regret treating Lefschetz pencils only in the case of fiber dimension 1. Apart from using derived categories and including Lefschetz pencils with arbitrary fiber dimension, I plan to keep the book much as before, but with the statements of the main theorems updated to take account of later work. Whether the new version will ever be completed, only time will tell.

1982 Hodge Cycles, Motives, and Shimura Varieties (with Pierre Deligne, Arthur Ogus, Kuang-yen Shih)

Lecture Notes in Math. 900, Springer-Verlag, 1982, 414 pages, ISBN 3-540-11174-3 and 0-387-11174-3
Usually out of print. List price 99.00 USD (paperback) Springer Available online at springerlink for 29.95 USD per section.

1986 Arithmetic Duality Theorems

Academic Press, 421+x pages, ISBN 0-12-498040-6. Out of print.
Proves the duality theorems in Galois, étale, and flat cohomology that have come to play an increasingly important role in number theory and arithmetic geometry,
2006 Second corrected TeXed edition (paperback).
Booksurge Publishing, 339+viii pages, ISBN 1-4196-4274-X
Available from bookstores worldwide. List price 24 USD. An online bookstore
The posted version (click 2006) agrees with published version except for the copyright page (for more information, see adt.html).

1990 Vol. I Vol. II Automorphic Forms, Shimura Varieties, and L-functions, (editor with L. Clozel)

Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 6--16, 1988.
Posted with the permission of Elsevier.
How I scanned these (since people keep asking). Comments on Copyright and Fair Use Law.

2006 Elliptic Curves

Booksurge Publishing, 246 pages, ISBN 1-4196-5257-5 (ISBN is for the softcover version).
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory.
Softcover version available from bookstores worldwide. List price 17 USD; an online bookstore.
Library of Congress Number (LCCN): 2006909782 (full data in process).
Some corrections doc

Following is the blurb for Elliptic Curves that was on Amazon, and would still be, but for the incompetence of the people at BookSurge/CreateSpace/Amazon.

This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in advanced undergraduate or first-year graduate courses.

Reviews
Indeed, the book is affordable (in fact, the most affordable of all references on the subject), but also a high quality work and a complete introduction to the rich theory of the arithmetic of elliptic curves, with numerous examples and exercises for the reader, many interesting remarks and an updated bibliography.
Mathematical Reviews, Álvaro Lozano-Robledo

J. S. Milne's lecture notes on elliptic curves are already well-known … The book under review is a rewritten version of just these famous lecture notes from 1996, which appear here as a compact and inexpensive paperback that is now available worldwide.
Zentralblatt MATH, Werner Kleinert

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