The XIII International Conference on Symmetry Methods in Physics (SYMPHYS-XIII) organized by the Bogoliubov Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research and International Center for Advanced Studies at Yerevan State University will be held in Dubna, Russia, July 6-9, 2009. The first five Conferences were organized by the Institute of Physics and Power Engineering in Obninsk from 1986 to 1991. The next seven Conferences of this series were held at the Joint Institute for Nuclear Research in Dubna: 1993, 1995 and 1997, at the Yerevan State University in Yerevan, Armenia 2001, 2003 and 2006 and at the Technical University, Prague, Czech Republic in 2004. The preliminary programme includes the following topics: Integrable and superintegrable systems; Symmetries of differential and difference equations; Lie groups, representation theory and special functions; Quantum groups and q-special functions; Foundations of quantum mechanics; Quantum optics, coherent states, Wigner distribution function; Symmetry in atomic and nuclear physics. The forthcoming SYMPHYS-XIII Conference is devoted to the memory of Professor Yurii Fedorovich Smirnov. Professor Yu.F.Smirnov (1935-2008) is a famous theoretical physicist. For a long time he worked at the Moscow State University. Professor Yu.F.Smirnov made a large contribution to the nuclear physics, and to investigation of various aspects of symmetries in Physics.