Some years ago a conference on l-adic cohomology in Oberwolfach was held
with the aim of reaching an understanding of Deligne's proof of the Weil
conjec- tures. For the convenience of the speakers the present authors -
who were also the organisers of that meeting - prepared short notes
containing the central definitions and ideas of the proofs. The
unexpected interest for these notes and the various suggestions to
publish them encouraged us to work somewhat more on them and fill out
the gaps. Our aim was to develop the theory in as self- contained and as
short a manner as possible. We intended especially to provide a complete
introduction to etale and l-adic cohomology theory including the
monodromy theory of Lefschetz pencils. Of course, all the central ideas
are due to the people who created the theory, especially Grothendieck
and Deligne. The main references are the SGA-notes [64-69]. With the
kind permission of Professor J. A. Dieudonne we have included in the
book that finally resulted his excellent notes on the history of the
Weil conjectures, as a second introduction. Our original notes were
written in German. However, we finally followed the recommendation made
variously to publish the book in English. We had the good fortune that
Professor W. Waterhouse and his wife Betty agreed to translate our
manuscript. We want to thank them very warmly for their willing
involvement in such a tedious task. We are very grateful to the staff of
Springer-Verlag for their careful work.