ANTS-IX was the ninth edition of the biennial International Symposium on Algorithmic Number Theory. The first edition of this symposium was held at Cornell University in 1994. ANTS-IX was held July 19-23, 2010 at INRIA in Nancy, France.

The ANTS-IX Program Committee consisted of 12 members whose names are listed on the next page. The selection of the accepted papers among the submissions was made from mid-January to end of March 2010. Each paper was thoroughly reviewed by at least two experts, including a Program Committee member. The Program Committee selected 25 high-quality articles, which are excellent representatives of the current state of the art in various areas of algorithmic number theory. The Selfridge Prize in computational number theory was awarded to the authors of the best contributed paper presented at the conference. We gratefully thank the authors of all submitted papers for their hard work which made the selection of a varied program possible. We also thank the authors of the accepted papers for their cooperation in the timely production of the revised versions.

Each submitted paper was presented by one of its co-authors at the conference. Besides contributed papers, the conference included five invited talks by Henri Darmon (McGill University), Jean-Fran¸cois Mestre (Universit´e Paris 7), Gabriele Nebe (RWTH Aachen), Carl Pomerance (Dartmouth College), and Oded Regev (Tel-Aviv University). We thank the invited speakers for having been able to provide abstracts of their talk, which are reproduced in this volume. This list of invited speakers originally included Fritz Grunewald (HHU D¨usseldorf), who unfortunately passed away on March 21, 2010, four months before the conference. A special lecture was held to honor his memory.

The conference organizers wish to thank all the people who made the conference possible. In particular, we gratefully acknowledge the support of the funding institutions.