09221 Abstracts Collection -- Algorithms and NumberTheory

From 24.05. to 29.05.2009, the Dagstuhl Seminar 09221 ``Algorithms and Number Theory \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available