FOREWORD 185Theory'' (the series of H. Iwaniec's lectures at Rutgers University): these notes con-
tain the most complete available account of the methods used in modern analytic
number theory, presented in the short and elegant style characterizing its authors.
I would like to thank the PCMI audience for its attention, its questions, and
its constructive criticism. I also thank the organizers, P. Sarnak and F. Shahidi and
the PCMI staff for the quality of the organization. Some parts of these notes were
written in june 2002 in Caltech under the invitation of D. Ramakrishnan and I thank
this institution for its hospitality and excellent working conditions. Thanks are due
to J. Cogdell, L. Clozel, E. Fouvry, G. Harcos, M. Harris, H. Iwaniec, E. Kowalski, D.
Ramakrishnan, P. Sarnak, J.-P. Serre, F. Shahidi and H. Stark for their explanations,
comments and corrections prior to, during, and after the writing of this text, and to
E. Royer and L. B. Pierce who have undertaken the painful task of correcting many
errors, inaccuracies and misprints of earlier versions; the ones that may remain or
that I may have added in the final version are my responsibility.